Cells are identical trigonal trapezohedron or rhombohedra. There are three special case geometries of the "diminished trigonal trapezohedron". The award is in the shape of the Shining Trapezohedron. A "truncated trapezohedron" has all vertices with 3 faces. A "trigonal trapezohedron" is an "isohedral rhombohedron". With D symmetry, it can be seen as an elongated trigonal trapezohedron. The "n"-gonal trapezohedron, antidipyramid, antibipyramid or deltohedron is the dual polyhedron of an "n"-gonal antiprism. As a trigonal trapezohedron, the cube is related to the hexagonal dihedral symmetry family. The truncated triangular trapezohedron is another polyhedron which can be formed from cube edge truncation. With pairs of triangles merged into rhombi, it can be seen as a trigonal trapezohedron. An "n"-gonal trapezohedron can be dissected into two equal "n"-gonal pyramids and an "n"-gonal antiprism. The deltoidal icositetrahedron, deltoidal hexecontahedron, and trapezohedron are polyhedra with congruent kite-shaped facets. Since all edges must have the same length, every trigonal trapezohedron is also a rhombohedron. If the polar vertices are completely truncated (diminished), a trapezohedron becomes an antiprism.