Uniform 2 k1 polytope


In geometry, 2k1 polytope is a uniform polytope in n dimensions constructed from the En Coxeter group. The family was named by their Coxeter symbol as 2k1 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-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-orthoplex in 5 dimensions, and the 4-simplex in 4 dimensions.
Each polytope is constructed from -simplex and 2k−1,1 -polytope facets, each having a vertex figure as an -demicube,.
The sequence ends with k = 6, as an infinite hyperbolic tessellation of 9-space.
The complete family of 2k1 polytopes are:
  1. 5-cell: 201,
  2. Pentacross: 211,
  3. 2 [21 polytope|221],
  4. 2 [31 polytope|231],
  5. 2 [41 polytope|241],
  6. 2 [51 honeycomb|251], tessellates Euclidean 8-space
  7. 2 [61 honeycomb|261], tessellates hyperbolic 9-space