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[1] 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)
- Catalan solids:
Simplicial tilings:
- Regular:
- Laves tilings:
Simplicial 4-polytopes include:
Simplicial higher polytope families:
- simplex
- cross-polytope (Orthoplex)
See also
Notes
- ↑ Polyhedra, Peter R. Cromwell, 1997. (p.341)
References
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