Icosiheptaheptacontadipeton

The icosiheptaheptaheptacontadipeton, or jak, also called the 221 polytope, is a convex uniform polypeton. It has 27 triacontaditera and 72 hexatera as facets, with 10 triacontaditera and 16 hexatera at a vertex forming a demipenteract as the vertex figure.

The icosiheptaheptacontadipeton contains the vertices of a hexateral prism.

Vertex coordinates
The vertices of an icosiheptaheptacontadipeton of edge length 1, centered at the origin, are given by:
 * (0, 0, 0, 0, 0, $\sqrt{6}$/3)
 * ($\sqrt{3}$/4, $\sqrt{6}$/4, $\sqrt{6}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/12) and all even sign changes of the first five coordinates
 * (±$\sqrt{2}$/2, 0, 0, 0, 0, –$\sqrt{2}$/6) and all permutations of first 5 coordinates

Representations
An icosiheptaheptacontadipeton has the following Coxeter diagrams:


 * x3o3o3o3o *c3o (full symmetry)
 * oox3ooo3ooo3oxo *c3ooo&#xt (D5 axial, vertex-first)
 * xox3ooo3ooo3oxo3ooo&#xt (A5 axial, hexateron-first)
 * xoxo ooox3oxoo3oooo3ooxo&#xt (A4×A1 symmetry, edge-first)
 * xo3oo3oo3ox3oo xo&#zx (A5×A1 axial)
 * xoo3oxo oxo3oox oox3xoo&#zx (A2×A2×A2 symmetry, hull of 3 orthogonal trigonal duoprisms)