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There are generic geometric names for the most common polyhedra. The 5 Platonic solids are called a ... 5 / 3 (3) 5 / 2 have some faces occurring as ...
Geometric variations with irregular faces can also be constructed. Some irregular pentahedra with six vertices may be called wedges. An irregular pentahedron can be a non-convex solid: Consider a non-convex (planar) quadrilateral (such as a dart) as the base of the solid, and any point not in the base plane as the apex.
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. There are only five such polyhedra:
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. ... (n−5)-face of the 5-polytope; Edge the ... Platonic solid ...
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices.
These lower symmetries allow geometric distortions from 20 equilateral triangular faces, instead having 8 equilateral triangles and 12 congruent isosceles triangles. These symmetries offer Coxeter diagrams: and respectively, each representing the lower symmetry to the regular icosahedron, (*532), [5,3] icosahedral symmetry of order 120.
5 Platonic solids: 4 Kepler–Poinsot ... in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, ... (non-Euclidean geometry) Isosceles ...
The relations can be made apparent by examining the vertex figures obtained by listing the faces adjacent to each vertex (remember that for uniform polyhedra all vertices are the same, that is vertex-transitive). For example, the cube has vertex figure 4.4.4, which is to say, three adjacent square faces. The possible faces are 3 - equilateral ...