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It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these:
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.
Numbering systems: W - number used by Wenninger in polyhedra models, U - uniform indexing, K - Kaleido indexing, C - numbering used in Coxeter et al. 'Uniform Polyhedra'. Number of vertices V, edges E, Faces F and number of faces by type. Euler characteristic χ = V - E + F
This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.
The numbers that can be used for the sides of a non-dihedral acute or obtuse Schwarz triangle that does not necessarily lead to only degenerate uniform polyhedra are 2, 3, 3/2, 4, 4/3, 5, 5/2, 5/3, and 5/4 (but numbers with numerator 4 and those with numerator 5 may not occur together). (4/2 can also be used, but only leads to degenerate ...
Polyhedron: Class Number and properties ... This List of uniform polyhedra by spherical triangle groups them by the ... order 120 2 3 | 5 - 3.10.10 W10, U26, K31, C29 ...
List of uniform polyhedra by Wythoff symbol. ... Polyhedron: Class Number and properties ... order 120 2 3 | 5 - 3.10.10 W10, U26, K31, C29 Truncated great ...
This category lists terms related to Polyhedra, for individual polyhedra see the sub categories: Category:Uniform polyhedra includes subcategories below AND 53 nonconvex forms: Category:Platonic solids for the five convex regular polyhedra. Category:Kepler–Poinsot polyhedra for the four non-convex regular polyhedra.