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simplicial polytope
In geometry, a simplicial polytope is a polytope whose facets are all simplices.
For example, a ''simplicial polyhedron'' in 3 dimensions contains only triangular faces〔Polyhedra, Peter R. Cromwell, 1997. (p.341)〕 and corresponds via Steinitz's theorem to a maximal planar graph.
They are topologically dual to simple polytopes. Polytopes which are both
simple and simplicial are either simplices or two-dimensional polygons.
== Examples ==
Simplicial polyhedra include:
* Bipyramids
* Gyroelongated dipyramids
*Deltahedra (equilateral triangles)
*
* Platonic
*
*
* tetrahedron, octahedron, icosahedron
*
* Johnson solids:
*
*
*triangular bipyramid, pentagonal bipyramid, snub disphenoid, triaugmented triangular prism, gyroelongated square dipyramid
* Catalan solids:
*
* triakis tetrahedron, triakis octahedron, tetrakis hexahedron, disdyakis dodecahedron, triakis icosahedron, pentakis dodecahedron, disdyakis triacontahedron
Simplicial tilings:
* Regular:
*
* triangular tiling
*Laves tilings:
*
* tetrakis square tiling, triakis triangular tiling, bisected hexagonal tiling
Simplicial 4-polytopes include:
*convex regular 4-polytope
*
* 4-simplex, 16-cell, 600-cell
* Dual convex uniform honeycombs:
*
*Disphenoid tetrahedral honeycomb
*
*Dual of cantitruncated cubic honeycomb
*
*Dual of omnitruncated cubic honeycomb
*
*Dual of cantitruncated alternated cubic honeycomb
Simplicial higher polytope families:
*simplex
*cross-polytope (Orthoplex)
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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