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Kaleido software indexing: K01–K80 (K n = U n–5 for n = 6 to 80) (prisms 1–5, Tetrahedron etc. 6+) Magnus Wenninger Polyhedron Models: W001-W119 1–18: 5 convex regular and 13 convex semiregular; 20–22, 41: 4 non-convex regular; 19–66: Special 48 stellations/compounds (Nonregulars not given on this list)
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
A regular polyhedron is identified by its Schläfli symbol of the form {n, m}, where n is the number of sides of each face and m the number of faces meeting at each vertex. There are 5 finite convex regular polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making nine regular polyhedra in all. In ...
A convex polyhedron is a polyhedron that bounds a convex set. Every convex polyhedron can be constructed as the convex hull of its vertices, and for every finite set of points, not all on the same plane, the convex hull is a convex polyhedron. Cubes and pyramids are examples of convex polyhedra.
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. Category:Archimedean solids for the remaining convex semi-regular polyhedra, excluding prisms and antiprisms.
Regular polyhedron. Platonic solid: . Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot ...
Self-intersecting 5-polytopes are also known as star polytopes, from analogy with the star-like shapes of the non-convex Kepler-Poinsot polyhedra. A uniform 5-polytope has a symmetry group under which all vertices are equivalent, and its facets are uniform 4-polytopes. The faces of a uniform polytope must be regular
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices , and 120 edges .