Uniform 1 K2 Polytope - Family Members

Family Members

The family starts uniquely as 6-polytopes, but can be extended backwards to include the 5-demicube (demipenteract) in 5-dimensions, and the 4-simplex (5-cell) in 4-dimensions.

Each polytope is constructed from 1k-1,2 and (n-1)-demicube facets. Each has a vertex figure of a {31,n-2,2} polytope is a birectified n-simplex, t2{3n}.

The sequence ends with k=6 (n=10), as an infinite tessellation of 9 dimensional hyperbolic space.

The complete family of 1k2 polytope polytopes are:

  1. 5-cell: 102, (5 tetrahedral cells)
  2. 112 polytope, (16 5-cell, and 10 16-cell facets)
  3. 122 polytope, (54 demipenteract facets)
  4. 132 polytope, (56 122 and 126 demihexeract facets)
  5. 142 polytope, (240 132 and 2160 demihepteract facets)
  6. 152 honeycomb, tessellates Euclidean 8-space (∞ 142 and ∞ demiocteract facets)
  7. 162 honeycomb, tessellates hyperbolic 9-space (∞ 152 and ∞ demienneract facets)

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