Pentacontatetrapeton

The pentacontatetrapeton, or mo, also called the 122 polytope, is a convex noble uniform polypeton. It has 54 demipenteracts as facets, with 12 joining at a vertex forming a dodecateron as the vertex figure.

It contains the vertices of an octadecadiminished pentacontatetrapeton, which consists of two triangular trioprisms where all the triangle bases are in opposite orientations. The remaining vertices form the 3 orthogonal hexagons of a hexagonal triotegum. It also contains the vertices of an inscribed dodecateric prism.

Vertex coordinates
The vertices of a pentacontatetrapeton of edge length 1, centered at the origin, are given by:
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt6}{4}\right)$$ and all even sign changes,
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0\right)$$ and all permutations in the first five coordinates.

Representations
A pentacontatetrapeton has the following Coxeter diagrams:


 * o3o3o3o3o *c3x (full symmetry)
 * xoo3ooo3oox *b3oxo3ooo&#xt (D5 axial, demipenteract-first)
 * ooxoo3ooooo3oxoxo3ooooo3ooxoo&#xt (A5 axial, vetex-first)
 * xoxoo3oxxoo xooxo3oxoxo xooox3oxoox&#zx (A2×A2×A2 symmetry)

Related polytopes
The pentacontatetrapeton is the colonel of a large regiment that includes 84 main members, 58 fissaries, and two pure compounds.