Pentacontahexahecatonicosihexaexon

The pentacontahexahecatonicosahexaexon, or lin, also called the 132 polytope, is a convex uniform polyexon. It has 56 pentacontatetrapeta and 126 demihexeracts as facets, with 7 of each at a vertex forming a birectified heptapeton as the vertex figure.

The pentacontahexahecatonicosihexaexon contains the vertices of a birectified hexacontatetrapetal prism, a cuboctahedral duoprismatic prism, a cubic-icositetrachoric duoprism, a hepteract, a small cellated octaexon, a triangular-small prismated hexateric duoprism, and a hexagonal-dodecateric duoprism.

Vertex coordinates
The vertices of a pentacontahexahecatonicosihexaexon of edge length 1, centered at the origin, are given by:
 * ($\sqrt{7}$/4, $\sqrt{3}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, ±1) and all even sign changes of the first 6 coordinates
 * (±$\sqrt{2}$/2, ±$\sqrt{2}$/2, ±$\sqrt{2}$/2, 0, 0, –0, ±1/2) and all permutations of first 6 coordinates
 * (3$\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, 0) and all even sign changes and all permutations of the first 6 coordinates

Representations
A pentacontahexahecatonicosihexaexon has the following Coxeter diagrams:


 * o3o3o3x *c3o3o3o (full symmetry)
 * oooo3oxoo3oooo3ooxo3oooo *c3xoox&#xt (E6 axial, pentacontatetrapeton-first)
 * xooox3ooooo3ooxoo *b3oxoxo3ooooo3ooxoo&#xt (D6 axial, demihexeract-first)