Simplicial polytope

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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.

Contents

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:

Simplicial tilings:

Simplicial 4-polytopes include:

Simplicial higher polytope families:

Notes

1. Polyhedra, Peter R. Cromwell, 1997. (p.341)

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References

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