Uniform 1 k2 polytope

In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n = k+4) 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 {3,3k,2}.

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)