Uniform 1 k2 polytope


In geometry, 1k2 polytope is a uniform polytope in n dimensions constructed from the En Coxeter group. The family was named by their Coxeter symbol 1k2 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequence. It can be named by an extended Schläfli symbol.

Family members

The family starts uniquely as 6-polytopes, but can be extended backwards to include the 5-demicube in 5 dimensions, and the 4-simplex in 4 dimensions.
Each polytope is constructed from 1k−1,2 and -demicube facets. Each has a vertex figure of a polytope, is a birectified n-simplex, t2.
The sequence ends with k = 6, as an infinite tessellation of 9-dimensional hyperbolic space.
The complete family of 1k2 polytopes are:
  1. 5-cell: 102,
  2. 112 polytope,
  3. 122 polytope,
  4. 132 polytope,
  5. 142 polytope,
  6. 152 honeycomb, tessellates Euclidean 8-space
  7. 162 honeycomb, tessellates hyperbolic 9-space

    Elements