Simplicial Polytope - Examples

Examples

Simplicial polyhedra include:

  • Bipyramids
  • Gyroelongated dipyramids
  • Deltahedra (Equilateral triangles)
    • Platonic
      • tetrahedron, octahedron, icosahedron
    • Johnson solids:
      • triangular dipyramid, gyroelongated square dipyramid, triaugmented triangular prism, snub disphenoid
  • Catalan solids:
    • triakis tetrahedron, triakis octahedron, tetrakis hexahedron, disdyakis dodecahedron, triakis icosahedron, pentakis dodecahedron, disdyakis triacontahedron

Simplicial tilings:

  • Regular:
    • triangular tiling
  • Laves tilings:
    • tetrakis square tiling, triakis triangular tiling, bisected hexagonal tiling

Simplicial 4-polytopes include:

  • convex regular 4-polytope
    • 4-simplex, 16-cell, 600-cell
  • 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:

  • simplex
  • cross-polytope (Orthoplex)

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