Classical mechanics also considers mathematically idealized extended materials as geometrically continuously substantial. Different implementations of these operators may create polyhedra that are geometrically different but topologically equivalent. The dot product may be defined algebraically or geometrically. Wormholes have been defined both "geometrically" and "topologically". In the second chapter he defines the integral both geometrically and analytically. There are infinitely many geometrically self-dual polyhedra. This is consistent with the behavior of a geometrically thick but simultaneously optically thin ring. This thus confirms that the original and normalized Euler spirals are geometrically similar. This includes convergent and convergent-divergent nozzles that may be fixed or geometrically variable. Geometrically frustrated systems in particular often exhibit residual entropy. This gives one way in which to visualize quotient spaces geometrically. Ordered topographies are defined as patterns that are organized and geometrically precise. Small and geometrically easy shapes may be produced with dry pressing. "z" is described by the equation formula 25 where formula 26 is determined geometrically. The action of is defined through the composition of three geometrically defined transformations.