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

Simplicial polyhedra include:

Simplicial tilings:

Simplicial 4-polytopes include:

  • convex regular 4-polytope
  • Dual convex uniform honeycombs:
    • Disphenoid tetrahedral honeycomb
    • Dual of cantitruncated cubic honeycomb
    • Dual of omnitruncated cubic honeycomb
    • Dual of cantitruncated alternated cubic honeycomb

Simplicial higher polytope families:

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See also

Notes

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

References

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


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