Simple polytope

Simple polytope

In geometry, a "d"-dimensional simple polytope is a polytope each of whose vertices is adjacent to exactly "d" edges.They are topologically dual to simplicial polytopes. The family of polytopes which are bothsimple and simplicial are simplices or two-dimensional polygons.

Examples

In three dimensions:
* prisms
* simple Platonic solids:
** tetrahedron
** cube
** dodecahedron
* simple Archimedean solids:
** truncated tetrahedron
** truncated cube
** truncated octahedron
** truncated cuboctahedron
** truncated dodecahedron
** truncated icosahedron
** truncated icosidodecahedron
* In general, any truncated polyhedron is simple, including examples:
** truncated rhombic dodecahedron
** Truncated rhombic triacontahedronIn four dimensions:
* 120-cell
* Tesseract (also 8-cell or 4-cube)
* simple [uniform polychoron] s:
** Truncated 5-cell
** Truncated tesseract
** Truncated 16-cell
** Truncated 24-cell
** Truncated 120-cell
** Truncated 600-cell
* In general, any truncated polychoron is simple.In higher dimensions:
* "d"-simplex
* hypercube

See also

* Dehn-Sommerville equations


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