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[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.