Simplicial polytope

In geometry, a simplicial polytope is a polytope whose facets are all simplices. For example, a simplicial polyhedron in three dimensions contains only triangular faces 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 bipyramids
 * 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, kisrhombille 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)