Simplicial polytope

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A d-dimensional simplicial polytope is a polytope whose facets are adjacent to exactly d ridges. They are topologically dual to simple polytopes. Polytopes which are both simple and simplicial are either simplices or two-dimensional polygons.

[edit] Examples

In three dimensions:

• simplicial Platonic solids:
  • tetrahedron
  • octahedron
  • icosahedron
• simplicial Catalan solids:
  • triakis tetrahedron
  • triakis octahedron
  • tetrakis hexahedron
  • disdyakis dodecahedron
  • triakis icosahedron
  • pentakis dodecahedron
  • disdyakis triacontahedron
• simplicial Johnson solids:
  • gyroelongated square pyramid
  • gyroelongated square dipyramid
  • triaugmented triangular prism
  • snub disphenoid

In four dimensions:

• 4-simplex
• 4-dim cross-polytope
• 600-cell

In higher dimensions:

• simplex
• cross-polytope

[edit] See also

• Simplicial complex