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Simplicial polytope

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Multicolored representation of a pentagonal bipyramid
Pentagonal bipyramid

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

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Simplicial polyhedra include:

Simplicial tilings:

Simplicial 4-polytopes include:

Simplicial higher polytope families:

See also

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Notes

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References

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  • Cromwell, Peter R. (1997). Polyhedra. Cambridge University Press. ISBN 0-521-66405-5.