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A pyritohedron is a dodecahedron with pyritohedral (T h) symmetry. Like the regular dodecahedron, it has twelve identical pentagonal faces, with three meeting in each of the 20 vertices (see figure). [3] However, the pentagons are not constrained to be regular, and the underlying atomic arrangement has no true fivefold symmetry axis.
The regular dodecahedron can be found in many popular cultures: Roman dodecahedron, the children's story, toys, and painting arts. It can also be found in nature and supramolecules, as well as the shape of the universe. The skeleton of a regular dodecahedron can be represented as the graph called the dodecahedral graph, a Platonic graph.
Other symmetry constructions of the rhombic dodecahedron are also space-filling, and as parallelotopes they are similar to variations of space-filling truncated octahedra. [12] For example, with 4 square faces, and 60-degree rhombic faces, and D 4h dihedral symmetry, order 16. It can be seen as a cuboctahedron with square pyramids attached on ...
The rhombicosidodecahedron shares its vertex arrangement with three nonconvex uniform polyhedra: the small stellated truncated dodecahedron, the small dodecicosidodecahedron (having the triangular and pentagonal faces in common), and the small rhombidodecahedron (having the square faces in common).
The stellation diagram for the regular dodecahedron with the central pentagon highlighted. This diagram represents the dodecahedron face itself. In geometry, a stellation diagram or stellation pattern is a two-dimensional diagram in the plane of some face of a polyhedron, showing lines where other face planes intersect with this one. The lines ...
The Schläfli symbol is a recursive description, [1]: 129 starting with {p} for a p-sided regular polygon that is convex.For example, {3} is an equilateral triangle, {4} is a square, {5} a convex regular pentagon, etc.
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