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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.
A chiliagram is a 1,000-sided star polygon. There are 199 regular forms [a] given by Schläfli symbols of the form {1000/n}, where n is an integer between 2 and 500 that is coprime to 1,000. There are also 300 regular star figures in the remaining cases. For example, the regular {1000/499} star polygon is constructed by 1000 nearly radial edges.
image of polyhedron; name of polyhedron; alternate names (in brackets) Wythoff symbol; 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.
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure : not itself an element of a polytope, but a diagram showing how the elements meet.
Quasi-regular polyhedra Johnson solids (92, convex, non-uniform) Bipyramids Pyramids Stellations: Stellations: Polyhedral compounds Deltahedra (Deltahedra, equilateral triangle faces) Snub polyhedra (12 uniform, not mirror image) Zonohedron (Zonohedra, faces have 180°symmetry) Dual polyhedron: Self-dual polyhedron
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).
Chiliagon - 1,000 sides; Myriagon - 10,000 sides; Megagon - 1,000,000 sides; Star polygon – there are multiple types of stars Pentagram - star polygon with 5 sides; Hexagram – star polygon with 6 sides Star of David (example) Heptagram – star polygon with 7 sides; Octagram – star polygon with 8 sides Star of Lakshmi (example) Enneagram ...