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 dipyramids
- Deltahedra
- * 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:
Simplicial 4-polytopes include:
Simplicial higher polytope families:
