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Four numbering schemes for the uniform polyhedra are in common use, distinguished by letters: [C] Coxeter et al., 1954, showed the convex forms as figures 15 through 32; three prismatic forms, figures 33–35; and the nonconvex forms, figures 36–92.
In all of these definitions, a polyhedron is typically understood as a three-dimensional example of the more general polytope in any number of dimensions. For example, a polygon has a two-dimensional body and no faces, while a 4-polytope has a four-dimensional body and an additional set of three-dimensional "cells". However, some of the ...
In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; [1] a three-dimensional solid bounded exclusively by faces is a polyhedron. A face can be finite like a polygon or circle, or infinite like a half-plane or plane.
Vertex the (n−5)-face of the 5-polytope; Edge the (n−4)-face of the 5-polytope; Face the peak or (n−3)-face of the 5-polytope; Cell the ridge or (n−2)-face of the 5-polytope; Hypercell or Teron the facet or (n−1)-face of the 5-polytope
The exterior face is a 60-90-30 triangle which is one-sixth of a tetrahedron face. The three faces interior to the tetrahedron are: a right triangle with edges , , , a right triangle with edges , , , and a right triangle with edges , , .
Edge, a 1-dimensional element; Face, a 2-dimensional element; Cell, a 3-dimensional element; Hypercell or Teron, a 4-dimensional element; Facet, an (n-1)-dimensional element; Ridge, an (n-2)-dimensional element; Peak, an (n-3)-dimensional element; For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and ...