text:
|Publication number
|Publication type
|Application number
|Publication date
|Oct 20, 1992
|Filing date
|Jun 6, 1991
|Priority date
|Aug 24, 1987
|Fee status
|Publication number
|Haresh Lalvani
|Original Assignee
|Haresh Lalvani
|Export Citation
|BiBTeX, EndNote, RefMan
|Patent Citations (9), Non-Patent Citations (2), Referenced by (13), Classifications (19), Legal Events (4)
|External Links: USPTO, USPTO Assignment, Espacenet
This application is a division of the application Ser. No. 07/428,018, filed Oct. 26, 1989, and now U.S. Pat. No. 5,036,635 which is a continuation of application Ser. No. 07/319,861, filed Mar. 6, 1989, and now abandoned which is a continuation of the application Ser. No. 07/088,308, filed Aug. 24, 1987 and now abandoned.
The invention relates to building systems for terrestrial and space architecture. More specifically the invention relates to periodic and non-periodic building systems using saddle polygons and saddle zonohedra derived from polyhedral stars. The saddle structures are used as tensile or shell-like surfaces which can be integrated with space frames.
The architectural environment has been, and it still is, dominated by plane surfaces and straight lines. These fall within the realm of Euclidean geometry. Plane curves, as in arches, and curved surfaces in valuted ceilings and domes, have been known for centuries and provide a necessary counterpoint to the rectilinear spaces. The domed surface, which is generally a sphere, is an example of a non-Eulcidean surface since the sum of the angles of a triangle on this surface is greater than 180°, while in plane geometry this sum is 180°. Such surface has a positive curvature while the plane has zero curvature. There is another class of surfaces which has a negative curvature and where the sum of the angles of a triangle is less than 180° . An example is the well-known hyperbolic paraboliod or hypar, or the hyperboloid of the nuclear power plants, for the pseudo-sphere. Non-Euclidean geometries were formalized in the last century and the names Lobachevsky, Bolyai, Gauss, and Reimann are associated with it. The spherical and the hyperbolic surfaces are doubly-curved. However, the two surfaces are different if we visualize them as being generated by two curves moving over one another. In spherical and ellipsoidal surfaces, the two generating curves are curved in the same way, while in the hyperbolic surfaces, the two curves are curved in opposite directions. The former as termed "synclastic", and the latter "anti-clastic", and both are curved space structures.
Though synclastic surfaces have been more commonly used in architecture, the use of anti-clastic surfaces has been increasingly seen only in the part three or four decades. The Catalan architect, Antonio Gaudi, first recognized its inherent structural potential as a "naturally" stiff or stronger surface, and his later work in the twenties molded the surfaces of stone into series of four-sided hyperbolic paraboloids in irregular compositions or linearly periodic arrays. Felix Candela, in Mexico in the fifties, used "hypars" (from hyperbolic paraboloids) as thin shell concrete structures in arrays of squares and a regular undulated octagon. Frei Otto in Germany, also in the fifties, used the minimal surface notion to develop his membrane structures. His studies with tensile fabric used single even-sided regular polygons with zig-zag edges in tension. Michael Burt in Israel, and Peter Pearce in the U.S., independently showed a systematic study of periodic saddle structures based on symmetry. Burt's saddle polyhedra, and their space-fillings are derived from regular and semi-regular polyhedra and their space-fillings, and have equal edges. Pearce's saddle polyhedra and their space-fillings are based on the cubic symmetry of his universal node system and use three lengths of edges. In marked contrast to these, some of Frei Otto's tent structures are non-modular are use irregular plane geometries to achieve architectural flexibility, an idea which is desirable in architecture. The first example of a doubly-curved shell structure based on the one-sided Mobuius surface was suggested by the Italian architect, Vittorio Giorgini.
In addition to the saddle polyhedra mentioned above, a new class of continuous period minimal surface were independently reported by Alan Schoen, Michael Burt and Peter Pearce. These are continuous saddle surfaces without self-intersections that divide space into two congruent or complementary spaces. The first example of a curved space labyrinth was discovered by Schwartz. A four-dimensional Schwartz surface was developed by David Brisson. A few additional curved labyrinths based on packings of Platonic and Archimedean polyhedra were discovered by Lalvani. The plane-faced and straight-edge structures related to these were reported jointly by Burt, Wachman and Kleinmann and are based on packings of regular and semi-regular polyhedra. These are composed only of regular polygons and are termed "infinite polyhdera". the known curved space labyrinths are based on the high degree of symmetry of periodic space networks from which they are derived and correspond to prismatic, tetrahedral and cubic symmetries where the prismatic symmetries correspond to the space-fittings of regular prisms, and the other two are based on the tetrahedron and the cube, respectively.
Prior art in curved space structures has two basic directions. The first using the non-modular, custom-tailored approach where the parts of a structure are shaped in response to architectural, functional, structural or aesthetic needs, which neccessitate an inherent flexibility in shaping spaces and where irregular planes, even in rectilinear buildings, are a result. In contrast to their, the thrust of industrialization in building has led to the notion of using mass-produced indentical parts for a built-in economy of design, production, construction, etc. This had led to the use of periodic structures based on symmetry. In the latter again, there are two approaches --one based on regular structures having equal edges and equal angles, as in the case of Burt, and the other developing a "unified" building system using at least three types of edges (lengths) but permitting recombinations of the same parts into a large variety of configurations as in the case of Pearce. Clearly, the latter approach is successful in providing a "flexible" system, and hence a flexiblity in the configurations it produces. Both approaches, clearly exploiting the advantages of periodicity to a great extent, have built-in restrictions. Periodicity is forced on the spaces generated, the spaces have "predetermined" proportions based on the symmetry from which they are derived, and many of the spaces have the regularity imposed by spherical or prismatic point groups of symmetry. Clearly, some of the properties may be advantageous in some situations and the experience of a sense of order and beauty that symmetry brings is desirable. But all periodic building systems reinforce the advantages of periodicity and deny irregular planes, or departures in directions of space here and there, and other such devices a designer finds useful. The repetitive nature of periodic structures often removes the element of surprise and intrigue in architecture, resulting in a loss of visual and experiential interest by users and observers.
The art of building would be furthered if all the advantages of periodicity were retained, and yet the irregularity was made possible, the proportions and shapes of space were not "dictated" by regular polygons, regular and semi-regular polyhedra, or proportions determined by high symmetry groups. The present disclosure is aimed in this direction. It uses modularity--one length of edge only as one possibility--excludes the use of regular polygons, permits infinite families of structures, permits periodic arrangements, and most important of all, it makes non-periodic, random-looking arrangements possible out of the same modules. The modules are based on minimal surface or its deformations and use a variety of saddle shaped components. A modular system that permits non-periodic curved space structures is not mentioned in the prior art, and a system that permits both periodic and non-periodic arrangements out of the same curved modules is also not mentioned in prior art. More specifically, the present invention described the derivation of saddle polygons and saddle polyhedra based on zonohedra and parallelopipeds.
U.S. Pat. No. 4,133,152 to Roger Penrose is cited for disclosing a non-periodic plane tiling based on pentagonal symmetry. U.S. Pat. No. 4,620,998 to H. Lalvani is cited for disclosing periodic and non-periodic plane tilings using crescent-shaped polygons. U.S. Pat. No. 3,931,697 to P. Pearce discloses periodic saddle configurations based on regular-faced polyhedra of cubic symmetry. U.S. Pat. No. 4,584,800 to M. Burt and E. Kent discloses a tension surface based on a periodic array of saddle hexagons. U.S. Pat. No. 3,663,346 to A. H. Schoen discloses periodic honeycomb structures based on cubic and prismatic symmetries. U.S. Pat. No. 3,970,301 to C. R. Lehmann discloses three-dimensional tensile nets based on periodic symmetries obtained from pachings of regular-faced polyhedra and prisms. U.S. Pat. No. 4,492,723 to L. S. Chadwick discloses polyhedral construction kits with curved faces and curved edges. U.S. Pat. No. 4,651,479 discloses four-sided hypars in a periodic hexagonal array. The French patent 2,453,5957 to C. Iconomou discloses four- and six-sided hypars as warped panel structures. The paper `Saddle Polyhedra` by Michael Burt, published in Zodiac 21, Olivetti Co., Italy (1973) and Peter Pearce's structures from his book `Structure in Nature is a Strategy for Design`, MIT press (1978), are also cited as prior work.
The term `zonohedra` is used here to describe `plane-faced` zonohedra, i.e. a class of known polyhedra with even-sided plane polygonal faces arranged in pairs of opposite and parallel faces. The faces of zonohedra are parallelograms and zonogons, where zonogons are even-sided polygons with pairs of opposite and parallel edges. The term `saddle zonohedra` will be used for polyhedra composed of saddle polygons and derived from zonohedra by the method described herein.
This application discloses the derivation saddle zonohedra from `polyhedral` n-stars (or n-vector stars), where n-star is a star of n non-collinear vectors radiating from a point. Polyhedral n-starts described here are obtained by joining the vertices of any polyhedron to its center. From each n-star, a class of sub-stars termed p-stars, where p is any number greater than two and less than or equal to n, is also used to derive zonohedral and saddle zonohedral structures. Three classes of polyhedral n-stars used in this invention are determined by:
i) an n-star with equal vectors based on an arbitrary or irregular polyhedron having a vertices lying on a sphere, with n greater than three;
ii) an n-star with equal vectors based on a regular or semi-regular polyhedron, polyhedral duals, and stars based on subdivisions of polyhedra, with 2 n vertices where n is greater than four;
iii) an n-star with unequal vectors based on an arbitrary or irregular, convex or non-convex polyhedron with n greater than 3.
The three classes of n-stars are hierarchical in their regularity. The stars based on regular or semi-regular polyhedra and the most ordered. The stars based on arbitrary spherical polyhedra have lost the regularity of angles. The stars based on arbitrary convex or non-convex polyhedra have lost the regularity of both lengths and angles. This class of n-stars further removes the restrictions of regularity already greatly reduced by the previous class. This produces modular saddle structures with unequal edges and arbitrary angles, and is the further from regular structures. Even when such regular or semi-regular stars are used as a starting point, as in the second class of polyhedral stars based on symmetric polyhedra, the end result is not regular at all, as any arbitrary composite of convex and non-convex saddle polygons within one saddle zonohedron can be derived.
In the present application, a large class of saddlle polyhedra with convex and non-convex saddle polygonal faces is disclosed. Sometimes, saddle faces are combined with plane faces. The space-fillings of these saddle polyhedra are also disclosed. These space-fittings are periodic or non-periodic. In the non-periodic cases, highly irregular looking configurations are possible. A special class of non-periodic structures which are periodic in one direction and non-periodic in another are also disclosed. Curved space labyrinths based on a saddle variant of a truncated octahedron are also disclosed. Saddle polyhgons defined by the edges of non-periodic space-fillings or parallelopipeds or rhombohedra are also disclosed. The saddle polyhedra described herein can used as tensile structures by themselves, or in combination with space frames, or as shell-like surface structures. Though only selected examples are shown as embodiments of the invention, numerous variants can be derived without departing from the scope of the invention as described herein and appended by the attached drawings.
Referring now to the drawings which form a part of this disclosure:
FIG. 1 shows the derivation of various saddle polyhedra from a 4-vector star (p=4). Included are saddle tetrahedra composed of four saddle hexagons, and others which use a combination of plane and saddle polygons.
FIG. 2 shows periodic space-fillings of various saddle polyhedra of FIG. 1 including saddle tetrahedra, a hexagonal prism with saddle top and bottom, and a saddle hexahedron. Periodic but sheared variants of the diamond lattice as are also shown.
FIG. 3 shows miscellaneous saddle polyhedra from a 5-vector star (p=5,n=15) obtained from a semi-regular polyhedron.
FIG. 4 shows the space-fillings of saddle polyhedra based on 5-stars (n=5).
FIG. 5 shows the derivation of saddle polyhedra from a 6-star (n=6). This includes saddle variants of the truncated octahdedron composed of eight saddle hexagons and six parallelograms.
FIGS. 6a and 6b show space-filling of saddle polyhedra of FIG. 5/ Included are examples of a curved space labyrinth as anon-regular variant of the known Schwartz surface. Periodic and non-periodic configurations are suggested.
FIG. 7 shows the method of deriving composite n-stars by adding stars with the example of an irregular, layered, non-periodic variant of the diamond lattice and the associated space-filling of saddle polyhedra.
FIG. 8 shows an example of various saddle octahedra composed of eight hexagonal saddles from a star that changes n from 4 through 6. The corresponding space-fillings are also shown.
FIG. 9 shows a portion of a non-layered non-periodic space lattice composed of inclined parallelopipeds or rhombohera, and an associated saddle of surface composed of saddle hexagons based on a 6-star.
FIG. 10 shows two other examples based on the non-periodic lattice of FIG. 9. The configuration on top uses octagonal saddles inscribed within parallelopipeds. The configuration below is a curved varaint of the one above.
FIG. 11 shows a portion of a non-periodic lattice based on a slight variant of 6-star of FIG. 9. A special non-regular continuous curved surface with a "hole" is derived from edge-to-edge connected parallelopipeds (or rhomboherda) and is composed of octagonal saddles.
FIG. 12 shows an extension of the continuous curved surface of FIG. 11. Poosibilities for stacking saddle modules is also shown.
FIG. 13 shown one example of a centrally or spherically symmetric saddle zonohedron of icosahedral symmetry based on a 10-star obtained from a regular dodecahedron.
FIG. 14 shows the decomposition of an inclined parallelopiped into smaller inclined parallelopipeds as a basis for periodic sub-arrays of saddle polygons within periodic, non-periodic or centrally symmetric arrays.
FIG. 15 shows some candidate concepts for the integration of structural system with the geometry of saddle polyhedra shown in the previous figures. Examples of rigid frames, hinged space frames, tensile membranes, use of cables, and the application of a multi-level, non-planar, layered frame configuration to a "horizontal surface" is also shown.
In FIG. 1, 2 is a 4-star or 4-vector star (i.e., n=4 case) based on an arbitrary tetrahedron and having 4 vectors q, r, s and t. The four vectors may or may not be equal in length, and the angles between these vectors are unequal. The tetrahedron can be visualized by joining the four outer ends of the four vectors to one another such that C is its center. When the vectors are equal, the vertices of the tetrahedron lie on a sphere. The 4-star 2 produces the zonohedron 3, shown here with the 4-star in its interior which subdivides the zonohedron into four rhombohedra. In 4, the zonohedral shell is shown. Its edges are equal and parallel to the corresponding vector directions as marked. This particular zonohedron is a deformed rhombic dodecahedron, where the undeformed one is a well-known Archimedean dual polyhedron. The three rhombii surrounding each of its four tri-valent vertices can be replaced by four saddle hexagons, where each saddle hexagon is the zig-zag "girth' polygon of each rhombohedron. This is shown by heavy lines in 4 and is shown separately in 5. The skeletal configuration 5 can act as the edges of a non-convex polyhedron as shown in 6 and 7. This non-convex polyhedron is irregular saddle tetrahedron in both cases and is composed of 4 saddle-shaped hexagons. In 6, each saddle hexagon is composed of six planar triangular regions 19a, 19b and 19c as shown. In 7, the saddle hexagon is a familiar smooth minimal surface, characteristic of soap films, and used as a starting point for membrane structures. In practice, the minimal surfaces are deformed due to gravity. However, in the zero-gravity envirnments of space, true minimal surfaces can be achieved
8-12 are various examples of saddle polyhedra obtained from 4 by replacing a set of even number of contiguous edges of the zonohedron with a saddle polygon. Examples 8-11 combine plane rhombic or paralellogram faces with saddles. 8 and 10 are non-regular zig-zag hexagonal prisms with saddle hexagonal tops and bottoms. 9 is a variant on the hyperboloid and is capped by three rhombii 24a, 24b and 24c on either sides. 11 is special variant of an inclined prism with saddles on either sides. 12 has saddles in an irregular composition, with or without plane rhombic faces.
13 and 16 are variants of the 4-star 2. In both variations, the vectors q, r and t are kept unchanged and the vector s has changed to s' and s" respectively. The corresponding skeletal edge configurations 14 and 17 correspond to 5, and the saddle tetrahedra 15 and 18 correspond to 7. In both variants, the saddle hexagon 21 remains unchanged, while the saddle hexagon 20 changes to 31 and 33, and 22 changes to changes to 32 and 34, respectively. These two variants suggest that other variations in the angles and lengths of vectors would produce variable geometries of saddle tetrahedra. All four vectors can be changed in an infinite variety of combinations, liberating the restriction of regularity with predetermined angles to any desired proportion of space or structure. For each 4-star, there are thus infinite positions, and hence an infinite variety of saddle structures can be produced for n=4 case.
FIG. 2 shows periodic space-fillings of saddle polyhedra based on n=4 case. 35 and 37 are titled or skewed variants of the diamond lattice. The lattice 35 is composed of wire-frame cells 5, and the lattice 37 is composed of cells 17. The corresponding periodic space-fillings of saddle tetrahedra are shown in 36 and 38, respectively. 36 is composed of saddle tetrahedra 7 and 38 is composed of 18. 39 is a periodic space-filling of zig-zag hexagonal prisms 10a which are variants of 10. 40 is a skeletal saddle hexahedron and a 4-star and is composed of six saddle hexagons. The corresponding saddle hexahedron 41 is a space-filling module as shown in the periodic array 42.
FIG. 3 shows various saddle polyhedra produced from a 5-star. This particular example is based on one example taken from the family of n-stars derived from any regular or semi-regular polyhedron. Since all the vertices of these polyhedra lie on the same sphere, this class of polyhedral stars are special cases of the one mentioned above. From an n-star, any p-star (where p is less than or equal to n) can be derived. When p=n, the zonohedron retains the spherical symmetry of the parent polyhedron from which the p-star is derived. But values of p less than n are less regular, though a few still retain some sub-symmetry. The present disclosure uses these zonohedra as an intermediary step to derive saddle polyhedra.
One example of p=5 from n=15, based on the star derived from icosidodecahedron, a well-known Archimedean polyhedron composed of alternating pentagons and triangles, is shown in 43 and 44. The five vectors u, v, w, x and y in 43 correspond to one pentagonal face 55 of the icosidodecahedron 56 shown in illustration 44. The five vectors produce the zonohedron 46 with twenty rhombic faces, with edge directions as indicated by five outer edges, and where all other edges are parallel and equal to these five edges. Variants can be derived by suitably changing the lengths and/or angles of the 5-star. An example is shown in 45 where the vectors have been changed to u', v', w', x' and y' and the plane pentagon 55 has transformed to a non-planar non-convex pentagon 55a.
The saddle zonohedra 47-51 are derived from 46 by replacing sets of contiguous rhombii by a saddle polygon. The saddle polyhedron 47 has a sinuous strip of rhombii removed and replaced by a non-convex saddle decagon 57. It has five such saddles in a five-fold rotational symmetry along the axis joining the two pointed apices. The saddle polyhedron 48 replaces every pair of adjacent rhombii by two types of non-convex saddle hexagons 58 and 59. It has ten such saddle hexagons. 49 is composed of at least three different saddle polygons. The hexagons 58 and 60 and the octagon 61. 50 is composed of saddle hexagons 60 and 62 and a saddle octagon 63. 51 is composed of saddle hexagon 60 and saddle decagon 64.
Saddle zonohedra 52-54 combine plane rhombic faces with saddles. 52 is related to 9 and has a girth hyperboloid 65 capped by pieces 69, each composed of rhombii 66 and 67. 53 is capped by decagonal saddles 68 on top and bottom and ten rhombic faces in the equitorial region. 54 is a decomposition of the zonohedron 46 by saddle polygons 71 lying on its interior. This particular example has two parallel saddle octagons 71 forming a zig-zag octagonal saddle prism 70 in the middle region. The top and bottom region are caps 69 composed of rhombii 66 and 67 on the outside and the octagon 71 on the inside.
Other saddle polyhedra from this and other p-stars and n-stars can be derived for each regular or semi-regular polyhedron. The present system uses such polyhedra with 2 n vertices with n greater than 4. This excludes three of the regular polyhedra, the tetrahedron, the octahedron and the cube. The remaining two, the icosahedron and the pentagonal dodecahedron, and the 13 Archimedean polyhedra can be used to derive an extremely large variety of saddle polyhedra by the method described. In addition, one polyhedral star can be combined with another by superimposing the two over each other to produce hybrid n-stars from which other saddle zonohedra can be derived. Spherical or polyhedral subdivisions, like the method used for geodesic spheres, lead to other classes of n-stars.
FIG. 4 shows examples of periodic lattices and associated space-fillings of saddle polyhedra for the n=5 case. The 4-star 2 of FIG. 1 is converted to the 5-star 72 by adding the fifth vector z. The lattice 35 of FIG. 2, which is based on the star 2, thus transforms to the lattice 73 which is based on 72. In 73, skeletal hexagonal prisms 80 are thus added in alternating layers between skeletal saddle tetrahedra 5. Correspondingly, the space-filling 74 comprises the saddle tetrahedra 7 alternating with the zig-zag prisms 10a. The lattice 75 is obtained by removing certain edges from 73 and consists of cells 81 which are composed of three octagons and a hexagon. The associated space-filling 76 is composed of saddle polyhedra 82. 77 and 78 shows two decompositions of the space-filling 74. In 77, the saddle tetrahedron is fused with the zig-zag prism to produce the module 83. In 78, the saddle tetrahedron 7 and the prism 10a are shown as separate modules. 79 illustrates a layer from the periodic space-filling composed of zig-zag octagonal prisms 70 based on the 5-star 43 as shown in FIG. 3.
FIG. 5 shows an example based on a 6-star 84 (n=6 case). It is based on six unequal vectors i, ii', iii', iv, v and vi at arbitrary angles. The star 85 is a different representation of the same vector star; here the vectors ii' and iii' are shown on the opposite side of C, and the outer form obtained by joining the outer points of the vectors defines an irregular octahedron. The dotted lines in 85 indicate another way of defining the outer shape of the star; in this particular instance, the dotted lines show five faces of an irregular icosahedron which is obtained when all six vectors are extended beyond the center to the opposite sides and the twelve outer vertices are then joined. The star 84 or 85 generates the zonohedron 87 having 30 rhombic faces, where the six outer edges are identified by corresponding vectors and where other edges are parallel to these six. This zonohedron is an irregular variant of the known Archimedean dual, the rhombic triacontahedron. From this saddle polyhedra can be derived as shown earlier for the n=4 and 5 cases.
One irregular saddle polyhedron 89, sown in its skeletal form in 88, is obtained by selectively replacing eight of the twenty tri-valent vertices of 87 by saddle hexagons 102-105. There are additional four hexagons on the other side in an inverse symmetry, making a total of eight saddle hexagons. In addition, this polyhdron has six plane rhombii, two each of rhombii 99-101. The structure is an irregular saddle variant of the known semi-regular polyhedron, the truncated octahedron, and can be termed a `saddle truncated octahedron`. Clearly, there would be infinite such arbitrary 6-stars, each producing their own uniquely deformed saddle truncated octahedra. As examples, the variant star 90 produces the skeltal variant 91 and its saddle version 92 corresponding to 88 and 89, respectively, and the star 93 produces 95 and 96. In both stars 90 and 93, vectors i, ii', iii' and iv remain unchanged, and vectors v and vi change to vii and vii in 90 and to ix and x in 93. The rhombic faces 99 remain unchanged while the other faces change.
Saddle structures 96-98 are other examples derived from 87. Structure 96 can be derived from 89 by keeping the rhombii 99-101 unchanged and removing the remaining edges. The resulting structure has one smooth continuous surface 106; this surface can be decomposed into eight hexagons, each with three concave curved edges which alternate with three straight edges. Structure 97 has six faces composed of three pairs of opposite faces, where each face is a saddle octagon. Structure 98 has four saddle faces of which only two, namely 103 and 105 are visible in the view shown. The back side has two additional saddle faces, 102 and 104. The four saddle faces correspond to four of the eight saddles in 89 and their centers define an irregular tetrahedron.
FIGS. 6a and 6b show examples of periodic and non-periodic space-fillings based on the saddle polyhedra of n=6 case shown in FIG. 5. Structure 110 is a periodic space-filling obtained by repeating the module 89, 111 is an interesting variant, where the configuration is treated as a continuous saddle surface such that the interior of one module flows into the next module. This is achieved when the rhombic faces 99', 100' and 101' are "empty" or removed, converting them into holes. The modules 89 are modified to 89' and the configuration produced is a saddle labyrinth that divides space into two congruent but separate parts. By varying the angles and lengths of the vectors, an infinite class of saddle truncated octahedra can be produced, each leading to a labyrinth with a different geometry. 112 shows the possibility of stacking any set of variants in any combination along the vertical or an inclined axis, and the entire set can then be repeated periodically in the horizontal plane. This produces a special class of structures which are periodic in one (or more) direction and non-periodic in the other. For example, if two layers of a lattice or a space-filling are named A and B, then a periodic layer is of the type ABABABAB . . . . . ., and non-periodic layering is of the type AABABBBAABA . . . . . . in 112, the modules 88, 91 and 94 are stacked. When a unit of stacked is repeated periodically, several possibilities arise. These are described next.
The variant modules of the type shown in 112 have varying widths, and if modules on one layer touch their neighbours, this is not guaranteed on the other layers which have different modules. When the widths of the modules are constrained to a fixed size A as shown in 113, where A specifies the width of the parallelogram passing through the middle of the module 89', module 115 in the lower layer has to have the same width A to gaurantee it will touch its neighbours when repeated in its layer. Two or more modules can be similarly stacked, in periodic or non-periodic manner along one direction, and repeated periodically along the other, in 113, when the rhombii are holes, a zig-zag variant of 111 is produced. The configuration 114 shows a portion of a periodic or non-periodic configuration where the modules 89' and 95' (i.e., 95 with rhombic faces removed) do not adjusted widths. The layer containing 95' touches its neighbours in the bottom layer, while the top layer containing the smaller modules 89' require the insertion of rhombic prisms 119 to make the space within adjacent modules continue from one to another.
In FIG. 6a, 114 is transformed to 115 by inserting the prism 120 between the top and bottom layers. Structure 116 is a variant of 115, where the module 96 replaces 89, 121 replaces 119, and 122 replaces 120. The connecting modules 121 and 122 are deformed hyperboloids with rhombic tops and bottoms.
FIG. 7 shows another example of a non-periodic lattice and space-filling for the n=6 case. This example, like some described in FIGS. 6a and 6b, is obtained by stacking a periodic layer with other layers in an periodic or non-periodic manner. When modules based on a different star are stacked, the lattice or space-filling has a composite value of n higher than the individual stars. The process of deriving composition n-stars is fundamental to deriving this class of layered non-periodic configurations and is shown in 123. Three related 4-stars, 2, 13 and 16 from FIG. 1, are added to obtain the star 126. The three stars have the vectors q, r and t in common, and the variant vectors s, s' and s" are added to obtain a 6-star as shown. Each individual layer of the lattice 124 is based on the individual stars, while the entire lattice is based on the composite star. Portions of only four layers are shown and the individual skeletal cells 5, 17, 14 and 5 (reading from top down) in each layer are shown. The associated space-fitting 125 is composed of corresponding saddle polyhedra 7, 33, 31 and 7. Compared with the sheared diamond lattice 35 or 37, this is an example of a non-periodic, irregular, layered diamond lattice.
FIG. 8 shows an example of topologically identical saddle polyhedra and their space-fillings based on a transforming n-star where n increases from 4 to 6. It is different from the examples shown so far where topologically identical saddle polyhedra were obtained from the same n-star. The 4-star 127 is composed of four vectors a, b, c and d. A fifth vector e is added to transform it to the 5-star 128. In the example shown, d has been tilted to d'. A sixth vector f is added to transform it to the 6-star 129. Clearly, the process of adding new vectors could be continued to higher values of n. The associated skeletal frames 130-132 for each of the three stars are shown alongside and make the process of transformation clearer. For each, the corresponding saddle polyhedra 133-135 are shown alongside. These saddle polyhedra are saddle octahedra and are composed of eights saddle hexagons.
Each saddle octahedron fills space periodically by itself or in non-periodic layers when alternated with layers or rows of other saddle octahedra. The periodic space-filling 136 is composed of 105. The configuration 137 shows the stacking of 133 on top of 134. When converted into a space-filling, both 133 and 134 can be repeated in their own layers periodically and the layers can be stacked periodicaly or non-periodically. Similarly, 135 and other variant modules can be introduced.
FIG. 9 shows a portion of a non-periodic lattice 139 composed of inclined parallelopipeds. It is based on the 6-star 138 composed of six vectors g, h, i. j, k and l of arbitrary lengths and arbitrary angles between them. When the lengths of the vectors are equal, the parallelopipeds become rhombohedra. The parallelopipeds in 139 are so arranged that planar layers do not exist in this particular example. All the parallelopipeds are tilted according the vector angles. Only eight parallelopipeds 142-149 of a space-filling lattice are shown in bold lines; the dotted lines extend the near faces (bolder lines) of the parallelopipeds. The edges of the parallelopipeds are marked by their corresponding vectors to which they are parallel and equal. The parallelopipeds or rhombohedra, obtained from p=3 stars, are the smallest zonohedral modules. The p=2 case makes a rhombus and no saddle structure is possible for p=2. For p=3, only one saddle zonohedron composed of three saddle hexagons, each obtained by removing one edge between three pairs of adjacent faces, is possible. The other examples are saddle polygons with six or either faces and are described next.
Configuration 141 is a portion of a non-periodic arrangement of saddle hexagons, where each saddle is bounded by the edges of one parallelopipeds. This is shown in 140 where an isolated saddle hexagon 149a is defined by six edges of the parallelopipeds 149. The edges are parallel to the vectors g, h and l. In 141, eight saddles 142a-149a are shown, each corresponding to the parallelopipeds in 139. The saddle 142a is defined by the parallelopipeds 142, 143a by 143, and so on.
FIG. 10 shows two more examples of saddle polygons inscribed within the parallelopipeds of 139. The configuration 151 is composed of rhombii 143b and 148b, and six octagonal saddles 142b, 144b-147b and 149b. A detail of 146b within the parallelopiped 146 is shown in 150. The configuration 153 is a curved variant of 151. Each octagonal saddle is converted into a saddle with curved edges as a shown in 152. The saddle 146b is transformed to 146c by converting each right-angled frame into a curved segment. Four curved segments define the boundary of 146b which is composed of alternating pairs of upward-facing curves 154 and downward-facing curves 155. 154 lies on the upper half of the face of the parallelopiped and 155 lies on the bottom half of the adjacent face. The plane view of 146c is a rhombus or a parallelogram, and is a skewed variant of the familiar hyperbolic paraboloid. Any suitable quadric or super-quadric curve could be used as a generator for this type of saddle surface. In 153, the saddles correspond to 151 in a one-to-one manner. The modules 143c and 148c are synclastic and doubly-curved in the same direction, and the remaining six modules are anti-clastic surfaces.
FIG. 11 shows a portion of a non-periodic space lattice 157 based on the 6-star 156 which is variant of the star 138. The six vectors directions are g, h, i, j, k' and l as before, with the difference that the vector k' is a shorter than k. The vectors associated with the edges of 157 are marked. In addition, six inclined parallelopiped cells 161-166, shown embedded in 157, are isolated in 158. The interior space between the six cells is a "hole". These six cells provide the framework for six saddle octagons 161a-166a in the configuration 160. 160 is a continuous surface with a hole 167a. The saddle octagons are the type 150 of FIG. 10. A detail of two adjacent saddles, 163a and 164a, is shown in 159. The edges are identified by their corresponding vectors, and the two share a common edge 168. The edge 168 can be seen on the bottom right between two edge-to-edge-connected parallelopiped cells 163 and 164. The edge-to-edge connection between two adjacent cells permits a smooth undulating surface between the two as seen in 159.
FIG. 12 is an extension of FIG. 11. The configuration 160 of FIG. 11 has been extended, and can be continued by adding extensions like 174-176 and by creating new holes like 173. The configuration 172 is an alternative obtained by introducing the stacking of modules on top of one another, i.e. saddles are defined by parallelopipeds or rhombohedra connected face-to-face. Two possible stackings are shown in 170 and 171. The top modules 177 are the same in each case, but the bottom modules are two different saddles 163a and 163b obtained from the same cell 163. 171 is "tubular" and is a continuous hollow surface. 172 is a portion of a non-periodic configuration with holes 178-80, with stackings of the types 170 and 171, and with smooth transitions of the type in 159.
FIG. 13 shows a one example of a saddle zonohedron with spherical or central symmetry based on a 10-star. The 10-star 181 is derived from the ten directions determined by the vectors xi-xx which join the center of a regular pentagonal dodecahedron to its vertices; the dodecahedron is a regular polyhedron composed of twelve pentagons and twenty vertices. The vectors corresponding to the edges are marked. The zonohedron 182, shown along its 5-fold axis of symmetry, has icosahedral symmetry and is composed of 90 rhombic faces. It consists of two types of rhombii, one comprising sixty rhombii grouped in twelve sets of five around the 5-fold vertices marked 183, and the other comprising thirty rhombii 184 located perpendicular to the 2-fold axes of symmetry and between two of the former sets. A saddle zonohedron 185 is obtained from 182 by converting the sets of five rhombii around the vertices 183 into twelve saddle decagons 186. In 185, three saddle decagons meet at the 3-fold vertices, and each pair of saddle decagons is separated by the rhombii 184 which remain unchanged. 187 is a different view of 185.
Other examples of saddle zonohedra from icosahedral symmetry include interesting cases from a 15-star, a 30-star, two different types of 60-stars, a 120-star and various combinations of these. From octahedral symmetry, the 13-star is an interesting generator for saddle zonohedra. The duals of semi-regular polyhedra retain the symmetry, but have different lengths of vectors. Non-convex polyhedra, like the uniform polyhedra or Kepler-Poinsot stellated polyhedra expand the geometry of stars. In addition, an infinite class can be derived from the various classes of geodesic spheres. Such spherical subdivisions, based on the sphere-projection of regular or semi-regular polyhedra followed by their subdivision, produce a large number of generator n-stars for saddle structures. From each, sub-stars can be obtained from all values of p greater than two and less than or equal to n. In all cases from symmetric stars, the derived saddle zonohedra may retain the symmetry, be partially symmetric or may be completely asymmetric. Further, combinations of convex, non-convex or plane parallelograms may be used as shown for examples based on 4-, 5- and 6-stars in FIGS. 1, 3 and 5, respectively. The possibilities increase by arbitrary stars. When the vectors are equal, the radiating vectors lie on a sphere. However, when the vectors are not equal, the polyhedron may be totally irregular or non-convex.
FIG. 14 shows two examples where the inclined parallelopiped (or a rhombohedron) is subdivided periodically into smaller parallelopipeds within which saddle polygons are introduced. 188 show five parallelopipeds from 151, where 142b is shown dotted and where each is subdivided into four smaller parallelopipeds 190. Each smaller parallelopiped contains a saddle octagon 191 of the type 150 of FIG. 10. In 189, a parallelopiped (shown in dotted) is converted into eight smaller parallelopipeds 192, each containing a saddle hexagon 193 of the type 140 of FIG. 9. These illustrations suggest the possibility of subdividing parallelopipeds or rhombohedra into smaller ones in a periodic manner, enabling the possibility of developing configurations which are periodic within the parallelopipeds but the parallelopipeds are arranged non-periodically. Such configurations are locally periodic but globally non-periodic. Alternatively, the subdivided parallelopipeds could be used in arrangements with an overall central symmetry.
FIG. 15 shows examples of integration of saddle surfaces with space frames. In building structures, saddle surfaces can be used as shells, either precast of cast-in-place, or as tensile surfaces. The tensile surfaces can be cable nets or membranes. The tensile surfaces can have free edges, or the edges can be constrained by a rigid frame. When used in combination with space frames, the membranes can be used a enclosing or space-defining surfaces, or as structural element which contributes to the stability of the frame. In the examples shown, the nodes of the space frame will have to be rigid in certain planes. When nodes are designed as free hinges, the well-known technique of triangulating the space frames could be used. This could be achieved by introducing diagonal braces of tensile cables as appropriate. The examples 194-200 show a selection of possibilities.
The structure 200 shows a tubular rigid frame 201 to which the edges of the saddle surface 146b is attached. The corners 202 are fixed and resist bending deformation. In contrast, the structure 195 shows the same saddle surface 146b held within a space frame configuration composed of struts 203 and nodes 204. The nodes permit rotation and diagonal struts 205 are introduced as stabilizers. In 196, the framing members 206 are connected to one another without visible nodes, but are free to move at the corners when subjected to forces. In this example, tension cables 207, anchored to fixed points 208, provide the needed stability. Only two saddle modules 196 and 197 are shown, and the dotted lines 209 indicate the positions of neighbouring modules. The fixed points 208, defined by the vertices of a portion of a non-periodic space lattice in this case, are thus determined by the vertices of adjacent parallelopipeds. This condition may be relaxed where other structurally favorable attachment points are available in the configuration.
The configuration 197 shows the structural framing of the six saddles 161a-166a from earlier configuration 160 in FIG. 11. The rigid frame of the type 194 is used in this example. The structure has five different levels which are marked by the points L0, L1, L2, L3 and L4. The level L0 is the "ground" level and marks a horizontal plane. L4 is the highest level of the structure. The vertical columns or posts marked B, B' and C are added to the configuration 160 to carry the weight to the level L0. These are continuations of the edge framing members. The columns B and B' mark the vertical direction. The columns B' are added to facilitate the transfer of weight from the inclined edges of the saddles.
The structures 198 and 199 show the use of tensile membrane surfaces with free edges within a space frame. The edges can use tensile cables to resist tear. The space frame is similar to 195 but no diagonal members are shown; rigid joints may be used instead of hinged nodes. In 198, the attachment points 210 of the membrane 211 are in the middle of the struts 203. In 199, the saddle 212 is of the type 140 of FIG. 9 but has free edges 213 separated from the struts 203 and is connected only at six nodes 204. The free edges can be converted into edge-cables to resist tension of the periphery of the membrane. In the structure 200, the non-periodic configuration 139 of FIG. 9 is converted to a space frame with struts 203 and nodes 204 and tensile membranes 142d and 144d-147d are inserted in five of the seven parallelopipeds. The other two, 143e and 149e, are shown without a membrane. The membranes are shown with free edges 213. The parallelopipeds correspond to the those in 139, and the configuration is a small portion of a space-filling structure.
|Cited Patent
|Filing date
|Publication date
|Jun 17, 1966
|Feb 20, 1968
|Timmy E. Wright
|Nov 27, 1968
|Mar 9, 1971
|Jesse R Hale
|Structural system utilizing membrane structural panels having double ruled quadric surfaces
|Aug 19, 1968
|Aug 24, 1971
|Peter J Pearce
|Synthesized natural geometric structures
|May 13, 1974
|Dec 16, 1975
|Synestructics Inc
|Modular curved surface space structures
|May 13, 1974
|Jan 13, 1976
|Synestructics, Inc.
|Modular curved surface space structures
|Jun 24, 1976
|Jan 9, 1979
|Roger Penrose
|Set of tiles for covering a surface
|Dec 15, 1980
|May 8, 1984
|Allied Corporation
|Tetrahedral truss
|Feb 5, 1985
|Nov 4, 1986
|Haresh Lalvani
|Crescent-shaped polygonal tiles
|Jan 29, 1986
|Aug 18, 1987
|Mccormick Donald M
|Geometric construction system and method
|Structure in Nature is a Strategy for Design by P. Pearce ©1978 pp. 86-127, 224-226.
|Structure in Nature is a Strategy for Design by P. Pearce 1978 pp. 86 127, 224 226.
|Citing Patent
|Filing date
|Publication date
|Mar 1, 1994
|Jul 11, 1995
|Jones; Richard H.
|Construction system
|Oct 21, 1992
|Sep 12, 1995
|Lalvani; Haresh
|Periodic space structures composed of two nodal polyhedra for design applications
|Jun 15, 1994
|Jul 30, 1996
|Smith; A. Graeme
|Plant cover
|Apr 7, 1995
|Mar 18, 1997
|Jones; Richard H.
|Construction system
|Mar 20, 2003
|Mar 22, 2005
|Tom Barber Design, Inc.
|Structures composed of compression and tensile members
|Oct 11, 2002
|Aug 30, 2005
|Yossi Amir
|Amir concept structures
|Sep 13, 2003
|Apr 18, 2006
|Thomasson Daniel E
|Geometric craft and educational kit
|Feb 24, 2011
|Jun 24, 2014
|Impossible Objects Llc
|Foldable construction blocks
|Dec 5, 2013
|Sep 9, 2014
|Stephen L. Lipscomb
|Web or support structure and method for making the same
|Dec 22, 2010
|Feb 24, 2015
|Liberty Diversified International, Inc.
|System and method for structure design
|Oct 11, 2002
|Apr 15, 2004
|Yossi Amir
|Amir concept structures
|Jun 23, 2011
|Jonas Hauptman
|System and method for structure design
|Aug 25, 2011
|Robert Swartz
|Foldable construction blocks
|U.S. Classification
|International Classification
|Cooperative Classification
|European Classification
|Apr 22, 1996
|Fee payment
Year of fee payment: 4
|May 16, 2000
|Maintenance fee reminder mailed
|Oct 22, 2000
|Lapse for failure to pay maintenance fees
|Dec 26, 2000
|Expired due to failure to pay maintenance fee
Effective date: 20001020


text:
CONCORD, N.C. -- Ryan Newman has an engineering degree from Purdue, so he can do the math.
Take 150 points from Clint Bowyer for having a car out of tolerance after Richmond, where the Richard Childress Racing team was warned, instead of the following week at New Hampshire, and Newman would have made the Chase by eight points.
Take the 577 points Newman accumulated through the first four races of the Chase with the 10 bonus points he would have from his win at Phoenix, and Newman would be in fifth place, 86 behind four-time defending Sprint Cup champion Jimmie Johnson.
"Yeah, I know," Newman said as he prepared for Saturday night's race at Charlotte Motor Speedway, where he typically is strong.
It would be easy for Newman to feel anger or disappointment that Bowyer was only warned at Richmond because it's not often you have a championship-caliber team, and his definitely would be had he found a way into the Chase.
In four races, the No. 39 Stewart-Haas team has an average finish of 7.5, better than the top four of Johnson, Denny Hamlin, Kevin Harvick and Jeff Gordon, all at 7.75. Newman's average finish of 7.85 over the past seven races is a series best.
What if? What if?
"It's not the first RCR car that has been illegal," Newman said with a smile. "It's not going to be the last. You can have an illegal Hendrick car, you can have an illegal Penske car and a Gibbs car. It's just unfortunate the way it all worked out."
Funny, he didn't mention Stewart-Haas cars being potentially illegal.
"I'm sure NASCAR could find something we didn't do," Newman quipped. "I also skipped Roush and RPM. I was just using a few examples."
Glad we clarified that.
Maybe, this is an argument for expanding the Chase field to 15 drivers, as NASCAR is considering for next season. With Newman in contention, there would be five drivers within 86 points of the lead and six within 107.
Add 14th-place Jamie McMurray, with his solid Chase start and two wins during the regular season, and there'd be seven within 107.
Let's keep the focus on Newman. The turnaround of his team has been phenomenal. He's gone from six top-10s in the first 23 races to six in the past seven. He is the perfect example of a team peaking at the right time.
Well, almost the right time. He needed to peak a few weeks earlier to make this run more meaningful.
"Guys would be worried about us if we were in it," crew chief Tony Gibson said of the Chase. "That's been our deal. We never give up no matter what. ... Teams know that about us. They never count us out. It's pretty cool to steal points from those Chase guys."
If the right foot goes forward, then the left foot is going to follow. Our right foot is forward now. Next year it'll be our left foot.
"-- Ryan Newman
So what's the biggest difference in Newman's team now and in the summer months, when it averaged 18.0 during a 10-race stretch? A lot of little things to help aerodynamics and handling, the same things that have team owner Tony Stewart running so well.
Had Stewart not run out of gas a lap and a half from the finish at New Hampshire, he would have two Chase wins and be only 13 points out of the lead, instead of fifth and 107 back.
What if? What if?
Perhaps the biggest factor for Newman is pit stops.
"Our pit stops have been almost two seconds better the last few races," Newman said. "If you stop three times a race, that's six seconds. I can't make up six seconds over Jimmie Johnson. I'm just happy to be running with him now."
Newman could be running with Johnson for a championship if NASCAR had pulled the trigger and penalized Bowyer at Richmond, as some inside the garage will argue should have happened. But officials insist that car was legal, and the fact that they penalized Bowyer a week later makes it hard to dispute what they say.
Newman has been as critical of NASCAR as anybody, and he's not tossing any stones.
"It's part of racing," Newman said. "I still say we could have put ourselves in a better position to not have to rely on him getting fined 150 points. Yeah, he was warned at Richmond, but that's water behind the bridge.
"We were pretty good at this time last year, too, and didn't win anything."
Not really. Newman was in the Chase, but four races in he was 223 points behind Johnson with an average finish of 13.5.
The last time Newman was this strong at this point in the season was before the Chase era in 2003 at Penske Racing. He started the final 10 races with two wins -- he had eight on the season -- and six top-10s. His average finish during that stretch was an amazing 3.6.
His only finishes outside the top 10 during the final 10 were because of crashes at Atlanta and Homestead-Miami, so we know he has championship potential.
"We've established that," Newman said.
The focus now is the same as it is for half a dozen drivers that didn't make the Chase: Finish 13th in points. It doesn't carry the million-dollar bonus that the driver who finished 11th with a 10-driver field did in the first few years of the format, but it's the top goal available for non-Charsers.
Don't think drivers aren't paying attention to that, either.
"Yeah, you notice what's going on out there," said Joey Logano, 20th in points. "We're still racing for points. We pay attention to what other teams around us are doing. We want to finish as high as we can."
And they all want to build momentum for next year, so they don't have to play this "what if" game.
"If the right foot goes forward, then the left foot is going to follow," Newman said. "Our right foot is forward now. Next year it'll be our left foot."
Sounds like Newman learned a little philosophy in college, too.
David Newton covers NASCAR for ESPN.com. He can be reached at firstname.lastname@example.com.

subset: commoncrawl


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Best of August in Kansas City
It's time to bid a fond farewell to Summer, make plans for Back To School, and enjoy many wonderful family outings in KC! Don't miss these our Top Picks for August in Kansas City!
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Kangol boasts some of the most recognizable hat shapes in the world, like the timeless 504 and 507. While Kangol remains committed to their most popular styles, they also offer phenomenal shape options like trilbies, baseball caps, buckets, army caps, and pull-ons. Kangol doesn't have a narrow focus, anybody can find something that will flatter their face and match their fashion tastes. Here, hats are conveniently separated by their shape. Once you figure out what shape suits you best, check out the different color and design details to find the hat that's perfect for you!
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Middle School Summer Slide- Middle School students (grades 5-8) can participate online to review language arts and math content from the past school year or to preview language arts and math content for the upcoming school year. $50 per student- click here: MS Summer Slide
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Welcome to Norton City Schools! Parents of students residing within the Norton City School district may print enrollment packets by clicking link above or packets may also be picked up at the Administration Office all summer. Select link for more details....


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hy all, i am using wp-mediamag theme.
The issue is i have enabled the fetured articls option from the theme dashboard, but it shows a blank area instead of the slider..
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text:
SMPTE Educational Webcast: Digital Content Storage in a Petabyte World
Thursday, March 8, 2012 at 1:00 PM (EST)
Event Details
Topic: To Have and Have Not: Digital Content Storage in a Petabyte World
Thursday, 8 March 2012
18:00 UTC /10:00 Pacific/13:00 Eastern
Login Details to Be Provided
Guest Speaker: Tom Coughlin, Coughlin Associates
Large rich media projects are getting ever bigger and raw content of multiple petabytes is becoming more common. Managing and protecting this content is a challenge and it is often a question whether backed up data can be recovered if the original copy is lost. Our presenter will explore developments in storage devices and systems used in modern digital workflows. These new developments are enabling accelerated collaborative media projects with ever larger source materials. Mr. Coughlin will also explore methods for creating, organizing and protecting rich media content including flash memory, local disk, digital tape and storage in the cloud.
Please join us for this very timely PDA Now educational webcast!
Thursday, March 8, 2012 at 1:00 PM (EST)
Add to my calendar
Winner of an Oscar® and multiple Emmy® Awards, the Society of Motion Picture and Television Engineers® (SMPTE®) is a global leader in advancing the art, science, and craft of the image, sound, and metadata ecosystem. A professional membership association that is internationally recognized and accredited, SMPTE advances moving-imagery education and engineering across the communications, technology, media, and entertainment industries. For a century, SMPTE has published the SMPTE Motion Imaging Journal and developed more than 800 standards, recommended practices, and engineering guidelines.
Nearly 7,000 members — motion-imaging executives, engineers, creative and technology professionals, researchers, scientists, educators, and students — who meet in Sections worldwide, sustain the Society. Through the Society's partnership with the Hollywood Professional Association (HPA®), this membership is complemented by the professional community of businesses and individuals who provide the expertise, support, tools, and infrastructure for the creation and finishing of motion pictures, television programs, commercials, digital media, and other dynamic media content. Information on joining SMPTE is available at www.smpte.org/join.


text:
Ramblin' Rose
|"Ramblin' Rose"
|Single by Nat King Cole
|Capitol Records
|Noel Sherman and Joe Sherman
|Lee Gillette
"Ramblin' Rose" is a 1962 popular song written by brothers Noel Sherman and Joe Sherman and popularized by Nat King Cole.[1]
Original song release[edit]
Cole's recording of the song was released by Capitol Records as catalog number 4804. It reached number two on both the Billboard and Cash Box charts and sold over a million copies as a single. In 1962 the song spent five weeks at number one on the Billboard Easy Listening chart and the Australian charts, while on the R&B chart, the song reached number seven.[2] It was released as a single from Cole's album of the same name, which also was a million seller. The song was nominated for a Grammy Award in the category Record of the Year.
Covers and similar songs[edit]
The song has been covered by many artists, particularly country music artists.
There are four country versions of the song. Sonny James recorded the song first in July 1968 and released it five years later on the album The Gentleman from the South in 1973.[3] Johnny Lee's version reached number 37 on the Billboard country chart in 1977.[4] The following year, singer Hank Snow's version charted at number 93.[5] In 1978, Johnny Rodriguez released a cover of the song on the album Love Me with All Your Heart.[6]
Petula Clark released a French version in 1962, titled "Les Beaux Jours". Her recording reached #10 in the French charts in 1963.[7]
Others recording this version of the song were Charley Pride 1962, Roy Rogers 1962, Billy Vaughn, Louis Armstrong, Bobby Vinton, Engelbert Humperdinck, Paul Anka, Floyd Cramer, Elvis Presley (home recording), Chuck Berry 1967, George Benson, the Mills Brothers, Dean Martin 1973, Marvin Gaye 1976, and Slim Whitman.
There is a different song called "Ramblin' Rose," recorded by Jerry Lee Lewis and MC5 in the 1960s; although it has the same title it is a different song, written by Wilkin and Burch, and not to be confused with the Nat King Cole hit.
Neither of those songs should be confused with "Rambling Rose," a light pop song from the 1940s, with music by Joseph Burke and lyrics by Joseph Allan McCarthy Jr. It has been recorded by a number of singers, most notably Perry Como.
See also[edit]
- ^ Gilliland, John (1969). "Show 22 - Smack Dab in the Middle on Route 66: A skinny dip in the easy listening mainstream. [Part 1]" (audio). Pop Chronicles. Digital.library.unt.edu. Track 5.
- ^ "Nat King Cole Top Songs". Music VF. 2016.
- ^ "Sonny James – The Gentleman From The South". Discogs. 2016.
- ^ "Johnny Lee Top Songs". Music VF. 2016.
- ^ "Hank Snow Top Songs". Music VF. 2016.
- ^ "Johnny Rodriguez (4) – Love Me With All Your Heart". Discogs. 2016.
- ^ Petula Clark: French chart hits
- Hyatt, Wesley (1999). The Billboard Book of #1 Adult Contemporary Hits (Billboard Publications)
External links[edit]
|Preceded by
"You Don't Know Me" by Ray Charles
|"Billboard" Easy Listening number-one single
by Nat King Cole
September 15, 1962 (five weeks)
|Succeeded by
"I Remember You" by Frank Ifield
|This pop standards-related article is a stub. You can help Wikipedia by expanding it.


text:
Foursquare © 2016 Lovingly made in NYC & SF
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Americas Best Inns-St. George, St. George
- Free continental breakfast, free WiFi, and free parking
Main amenities
- 49 guestrooms
- 4 restaurants
- Outdoor pool
- 24-hour front desk
- Air conditioning
- Self-serve laundry
What's around
- Heart of St. George
- Outlets at Zion (0.1 mi / 0.1 km)
- Red Cliffs Mall (1 mi / 1.6 km)
- Dixie State College of Utah (1 mi / 1.7 km)
- St. George Musical Theater (1.4 mi / 2.2 km)
- Hansen Stadium (1.5 mi / 2.4 km)
Americas Best Inns-St. George, St. George
Hotel Info: 866-539-8117from $59
- Suite, 1 King Bed, Jetted Tub
- Standard Room, 2 Queen Beds, Non Smoking
Also popular with travelers from the USA
At a glance
Key facts
Hotel size
- This hotel has 49 rooms
- This hotel is arranged over 2 floors
- Check-in time 2 PM-5:30 AM
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Required at check in
- Credit card or cash deposit required
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- Minimum check-in age is 21
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Travelling with others
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- Free WiFi in public areas
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Nearby Two Star St. George hotels
In the hotel
- Free continental breakfast
- 4 restaurants
- Outdoor seasonal pool
- Outdoor pool
- 24-hour front desk
- Laundry facilities
- Number of buildings/towers - 1
In the room
- In-room climate control (air conditioning)
- Air conditioning
- Coffee/tea maker
- Iron/ironing board
- Individually furnished
- Private bathroom
- Bathtub only
- Hair dryer
- 39-inch LED TV
- Pay movies
- Premium TV channels
- Free WiFi
- Free local calls
- Refrigerator
- Microwave
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Nearby hotels
Americas Best Inns-St. George, St. George's small print
Also known as
- Americas Best Inns St. George
- Americas Best Inns-St.
- Americas Best Inns-St. George
- Americas Best Inns-St. Hotel
- Americas Best Inns-St. Hotel George
- Americas Best Inns St. George Hotel
Please note: Maximum occupancy per room is 4 individuals, including children.
This property does not have elevators.
The name on the credit card used at check-in to pay for incidentals must be the primary name on the guestroom reservation.
Mandatory fees
The charges below are included in the total price displayed:
- Resort fee
We have included all charges provided to us by this hotel. However, charges can vary, for example, based on length of stay or the room you book.
Recent reviews
Good 3.8 /5 from 668 reviews
The hotel didn't have any frills, but was great for what we needed. Air conditioner worked great, which was very needed after being in the hot St. George sun. Beds were comfy. Lots of cable channels. It had all the basics and was mostly clean. The only thing was that I thought the carpet could use a shampoo. The staff was professional and friendly.
This hotel was wonderful. Everything, check-in, the rooms, the distance to shopping and the breakfast. The only thing I would improve on is maybe a bigger breakfast room.
The AC was very dirty. If you have allergy, it isn't your place. My wife got runny nose during our stays.
Spent one night with grand-kids. Room clean. Air conditioner did not work well, room very warm.
We booked on July 4th holiday weekend and it was big and comfortable bed. Booked online at hotels.com Two room suite for $110. Clean and on north end of St. George with new restaurants. Room was great, two tv, king size bed. Nice hotel clerk-Stacy-very knowledgeable.
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Use the tools below to refine your search by only displaying reviews with a certain number of star ratings or to only show reviews from a certain time period. Eg click on '1 star' to just display the reviews we have which received a 1 star rating click or 'Within the last month' to display just reviews posted over the last month.
Written on: 14/05/2015 by Sosadallofus (1 review written)
Have just booked what looked like a lovely holiday to Benalmedena for 4 adults and 1 child (albeit there are only 2 adults, 2 teens and 1 child). Total price comes up on screen and a reference number. Each time you google it a different price comes up but hey ho it wasn't a million miles off. First problem our return airport in Managua (which is in Nicuagra) instead of Malaga. Second issue is Agency bonding Fee of £18 per person per flight which is of course in the small print of the terms… Read Full Review
Written on: 19/05/2015
As a result of this review, we have been moved to a different hotel (we're told there have been a few problems with the hotel originally booked) all names on the booking have now been amended, a partial refund of the agency bonding fee has been made and a voucher issued towards the cost of our next holiday.
The manager who called was very helpful, even returning a call on his day off, and the refund was received by post within 24 hours.
Moral of this story...be sure to know the right questions to ask when making a booking (this was my first time of booking this kind of holiday). Check all fees are included in the TOTAL PRICE!!!
Overall, sales and management very helpful, admin poor. A whole lot of hassle but some confidence restored. We will see what the holiday brings.
Written on: 20/05/2015
I agree Cjd1959. Glad you had success with the management of 321travel. If 321travel made a few adjustments to their website and included the agency bonding fee on the front page in their total price they would have far less people ringing them up complaining as the customer could just click the button and finish the process without having to ring them at all. From all the review's I've read this charge seems to be a lot of the issues with 321travel. Also the only other problem with the website was that it didn't clarify that our booking was for 2 rooms. Other than that it would have been less stressful for us and also for them. It's making it very difficult for the management with the customer service when a few small adjustments would make it plainer to all involved.
Written on: 22/05/2015
We are sorry for the experiences you feel you had and are happy to see things have been sorted for you both. The peak period Bank Holidays always increase the call volume 100% as everyone is desperate to get away and the demand far out ways the supply. Admin lines can get very busy at these times of year but every issue will be sorted as soon as we can. Thank you for the positive feedback on the website and all comments regarding any improvements are always duly noted.
321 Travel.
Written on: 29/04/2015 by Holidayperson9 (1 review written)
I made a holiday booking with them last week and found it to be very simple and pleasant process and I would recommend to my friends… Read Full Review
Written on: 27/04/2015 by Daner424 (1 review written)
I got a holiday to lanzarote over a hundred pound cheaper than anywhere else, my flights on the way home stop via Dublin which is obviously the saving I couldn't get elsewhere but only 3 hours, bit annoying but worth the saving in my opinion. Hotel is all inclusive in the pocilos end of Porto Carmen which looks quite nice, all for less than 200 each. See how it goes but all positive so far! Also get vouchers for next holiday if I leave a review!… Read Full Review
Written on: 23/02/2015 by Benidormfor7 (1 review written)
I've just booked for a group of 7 ladies going to Benidorm in 2 weeks time, everything was done pretty quickly, would certainly use again… Read Full Review
Written on: 05/02/2015
Hi everyone who is tempted to use this company to book a holiday. I am sorry to disappoint you if you thought you had a hot deal from this them. They are most dishonest people I have ever had the misfortune to deal with. THE PRICE AGREED IS NOT WHAT YOU ARE GOING TO BE CHARGED FROM YOUR ACCOUNT IF YOU MADE A MISTAKE OF GIVING THEM THE CARD DETAILS WHICH THEY WILL PROMPTY ASK YOU TO PROVIDE IN ORDER TO BOOK FOR A DISCOUNTED HOLIDAY WHICH IS ACTUALLY NOT AVAILABLE. See my experience below and I… Read Full Review
Written on: 06/02/2015
Dear all
I am writing to give you an update on the above.
Furthermore, I got £50 refund and a £150 worth voucher for my next booking with 321 travel. I am overall very satisfied with the outcome of my complaint and very thankful to 321 Travel management for swiftly and satisfactorily dealing with this issue and more importantly for taking into account my feedback and that of other customers to improve the quality of their service.
Written on: 23/05/2015
same thing has just happened to me with this company totally disgusting
Written on: 21/02/2015
I was experienced almost the same,I phoned this company to book holyday in spain,the deal was cheap so I was happy to that deal,the man one Martin,said you should email the person who travel with you name and age etc,he given his email id,and he ask me the payment detail,and the payment detail given,next moment before sent email my detail,I have just checked this travels review,its so bad and horrible,so I call back and say please I don't want book,I change my mind not to travel now,then he said need £200 for cancellation fee.I wonder,because I didn't yet book with them and no details with them,even he have no proof where my address ,name ,nothing,I ask how can you to be take cancellation fee,if I booked the holyday,then cancel its fine but no booking been done.I check now my credit card statement,there is £200 deducted,now my bank dealing this case,I will go further to get back my money.
Written on: 13/04/2015
Hi, how would we get your card number if you did not make a booking? This post is a complete fabrication of the truth.
You booked a holiday and called back to cancel, as per our terms and conditions cancellation fees apply. I'm sorry if you feel this is unfair but this would be how every single Airline/Travel agent would work.
321 Travel.
Written on: 04/05/2015
Please contact Trading Standards with regards to this practise which is misleading. I have encouraged many individuals to do the same which is useful to aid Trading Standards in there investigation. I also recommend contacting Discount Center where they advertise this, they will be more than helpful as they have received a number of complaints.
Written on: 21/08/2015
They did the same to me. Cost me £1500.
Written on: 05/12/2014 by Egypt-is-where-I-went (1 review written)
I have just returned from Egypt, I got a great deal in a really nice hotel at a competitive price. I will be calling them again for my next trip… Read Full Review
Written on: 09/11/2014 by ginnep (1 review written)
I have traveled to Fuerteventura in the Canary and stayed at different hotel apartment and I can say this much I have enjoyed every moment of my time there. The island is quiet and the people are very friendly always smiling. There is so much to see and do. To top it you can take the ferry across to other island and make it two holiday in one. I am now planning my next holiday and cannot wait. This will be my 4th visit with many more plan. The fruits and veg are so fresh. The chipmunk are… Read Full Review
Written on: 19/08/2014 by 144Browne (1 review written)
Spent ages on ice lolly ringing for deals and couldn't find anything when I called but 321 did have a good look and the lady I spoke to spent a good hour towing and throwing trying to find something and in the end we found Majorca at the Bellevue that fitted my budget in August and I didn't think it would be do hard thought last minute was supposed to be where the deals where thankyou though… Read Full Review
Written on: 18/08/2014 by Majorcadeal (1 review written)
I've just secured my last minute Break to Majorca with the wife and 3 kids, great hotel, great price, great service and the wife's happy... So I'm happy!… Read Full Review
Written on: 05/07/2014 by dlRice330 (1 review written)
Please do not use this company, they promise so much, they do not give you the whole picture about your holiday, the additional charges it all ends up costing you much more than you planned. The bargain you think you got is nothing like that by the time you have finished! Then you have the awful challenge of their customer service to deal with, well the one person who seems to be running the show ... Mr Douglas. Go and find a company who actually cares about your holiday and will care when you… Read Full Review
Written on: 30/06/2014 by Gooddeal1 (1 review written)
I've just got the deal of the year, me and my wife with the 2 kids all inclusive for 1500 for 10 nights... They was so helpful I will be recommending them… Read Full Review
Written on: 30/06/2014 by MelanieHickey (1 review written)
Family of 4 to Tenerife for under 2k. Amazing, and very helpful too. Looking forward to it now… Read Full Review
Written on: 30/06/2014 by 410Wise (1 review written)
Booked we're third holiday to the Ibiza rocks with this company, simple process and emale the same day. Next it's time to pack and enjoy! A few keyboard warriors and trolls on this review centre !… Read Full Review
Written on: 09/09/2015
Really........You have been very lucky.........try sitting on a doorstep of a hotel for 11 hours cos they screwed up with their booking and there was not a room in the hotel to be had.........................I hope your next holiday is as good................GOOD LUCK WITH THAT...........PS I am not a troll just a customer who paid this company good money and they screwed it up !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Written on: 16/06/2014 by Italybreak (1 review written)
I have just returned from a 3 night city break with them, cannot fault there service, there got me there nice and cheap and all was as promised. Would recommend… Read Full Review
Written on: 13/06/2014 by patpotts (1 review written)
I am so happy someone sent me this chance to thank the company for arranging my fantastic trip. We went on a cheap cheap last minute budget for 8 people and got a very good deal. I was happy to travel from different airports, and even with the late change made I was still happy to proceed. Very smooth operation, sent the names by email, paid over the phone and all was done. Definably recommend to my community and friends. Thank you… Read Full Review
Written on: 11/06/2014
Just returned from a fantastic 2 nights in Venice.ist say cannot be more grateful of the team who helped me book this. Definitely going to reuse them for my main holiday in October… Read Full Review
Written on: 11/06/2014 by CarissaHoughton (1 review written)
Always the best prices for Ibiza, my third time using them for Ibiza now. It doesn't let me name the person I spoke to but very helpful guy I use every year. All smooth, I know the area and hotel are fine so will speak to you guys next year I guess!… Read Full Review
Written on: 09/06/2014 by hendo46 (1 review written)
first of all if you are thinking of booking a holiday with this company i would think twice my friends booked a holiday to sharm el sheikn a day later they ask me would i like to go with them yes i said so i rang 321travel ask them could i book a holiday to sharm el sheikn and could i be on the same flight as my friends i was told no problem and booked the holiday, when we got the flights information back we notice i had a difference flight number than my friends but they we leaving at the same… Read Full Review
Written on: 16/06/2014
We are very sorry to hear your experience and your geniune complaint. This matter is being looked into and a reply to your email should be with you soon so we can reach a resolution for you.
321 Travel.
Written on: 30/06/2014
I should have know better still waiting for your response as Ihave said before your customer service is rubbish I've been reading other customer reviews about you and they all say the same you are full of promises but you never deliver so mr Douglas let me see how long your so call customer service take to reply
Written on: 30/06/2014
If you want to only focus on the negative reviews as some people do, then yes. We send away many thousands of passengers each month without any problem and complaints are all relative to the passengers who travel. Any issue can take upto 28 days to reach a resolution after your complaint is registered and if you would like further help the TTA our trade regulator will be happy to help.
I just had a check at the Tesco reviews on here, 2 stars? Because mostly customers with any kind of problem will post online before a resolution is reached, I wouldn't call Tesco a bad company though.
321 Travel.
Written on: 15/05/2015
What a load of tosh. Tesco get two stars, you only avoid worse because you write your on reviews in order to cover up your bad ones. As for an office meeting, care to publish your office address?
Written on: 30/06/2014
After that reply I now know you know nothing
About costumer service you lot spoiled the first part of my holiday and I've already been in touch with a T V program about you and I'm coming down to your London office to see you face to face
Written on: 30/06/2014
We look forward to seeing you and in the meantime you can forward your complaint to the TTA who will be happy to help you as the trade regulator.
321 Travel.
Written on: 09/09/2015
Written on: 13/01/2015
They've took £200 out my account with out me nosing and won't refund it back. I'm going to trading standards about there conduct . I suggest you do the same. Don't let these people get away with it.
Written on: 28/01/2015
If, as you claim (and I don't believe you) they took £ 200 from your account without you NOTICING IT (you cant spell, you wrote 'nosing'), then simply contact your bank or credit card company and ask for a charge back.
Written on: 21/05/2014 by DaxEngland (1 review written)
The price was fine and that is the only positive thing I have to say about 321. The management of their office is unacceptable. They do not have the capacity to adapt to problems imposed on them by airlines. They are unable or unwilling to communicate effectively with their customers. This is after several requests of confirmed updates/changes to be e-mailed. Then the worse of all the issues I had with this firm, and there was many. Was on arrival to Spain. Finding out that the day I made the… Read Full Review
Written on: 28/04/2014 by Holiday99999 (1 review written)
I have just returned from a 3 day break in Spain booked with 321 Travel and I said I would write a review aslong as all went well, we had a great time and I roll recommend to my friends… Read Full Review
As rated by our community of reviewers
" Always Reliable " Read More
" Beautiful country, lovely people, amazing history " Read More
" Great holiday " Read More
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" Easy site " Read More