Simplicial polytope
![Multicolored representation of a pentagonal bipyramid](http://upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Pentagonale_bipiramide.png/220px-Pentagonale_bipiramide.png)
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[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[edit]
Simplicial polyhedra include:
- Bipyramids
- Gyroelongated bipyramids
- Deltahedra (equilateral triangles)
- Catalan solids:
Simplicial tilings:
- Regular:
- Laves tilings:
Simplicial 4-polytopes include:
Simplicial higher polytope families:
- simplex
- cross-polytope (Orthoplex)
See also[edit]
Notes[edit]
- ^ Polyhedra, Peter R. Cromwell, 1997. (p.341)
References[edit]
- Cromwell, Peter R. (1997). Polyhedra. Cambridge University Press. ISBN 0-521-66405-5.