Great prismatodecachoron

The great prismatodecachoron, or gippid, also commonly called the omnitruncated 5-cell, is a convex uniform polychoron that consists of 20 hexagonal prisms and 10 truncated octahedra. 2 hexagonal prisms and 2 truncated octahedra join at each vertex. It is the omnitruncate of the A4 family of uniform polychora.

This polychoron can be alternated into an omnisnub pentachoron, although it cannot be made uniform.

Like the omnitruncated simplex of any dimension, this polychoron can tile 4D space.

Vertex coordinates
The vertices of a great prismatodecachoron of edge length 1 are given by the following points, along with their central inversions:


 * (0, $\sqrt{2}$/3, –$\sqrt{3}$/3, ±2),
 * (0, $\sqrt{5}$/3, –5$\sqrt{5}$/6, ±3/2),
 * (0, $\sqrt{6}$/3, 7$\sqrt{6}$/6, ±1/2),
 * (0, 2$\sqrt{6}$/3, –$\sqrt{3}$/6, ±3/2),
 * (0, 2$\sqrt{6}$/3, –2$\sqrt{3}$/3, ±1),
 * (0, 2$\sqrt{6}$/3, 5$\sqrt{3}$/6, ±1/2),
 * (±$\sqrt{6}$/2, $\sqrt{3}$/6, –$\sqrt{6}$/6, ±3/2),
 * (±$\sqrt{3}$/2, $\sqrt{6}$/6, –2$\sqrt{3}$/3, ±1),
 * (±$\sqrt{10}$/2, $\sqrt{6}$/6, 5$\sqrt{3}$/6, ±1/2),
 * (±$\sqrt{10}$/2, ±$\sqrt{6}$/2, 0, ±1),
 * (±$\sqrt{3}$/2, ±$\sqrt{10}$/2, ±$\sqrt{6}$/2, ±1/2),
 * ($\sqrt{3}$/4, $\sqrt{10}$/12, –$\sqrt{6}$/3, ±2),
 * ($\sqrt{10}$/4, $\sqrt{6}$/12, –5$\sqrt{3}$/6, ±3/2),
 * ($\sqrt{10}$/4, $\sqrt{6}$/12, 7$\sqrt{3}$/6, ±1/2),
 * ($\sqrt{10}$/4, –$\sqrt{6}$/4, 0, ±2),
 * ($\sqrt{3}$/4, –$\sqrt{10}$/4, ±$\sqrt{6}$, ±1),
 * ($\sqrt{3}$/4, –7$\sqrt{10}$/12, –$\sqrt{6}$/6, ±3/2),
 * ($\sqrt{10}$/4, –7$\sqrt{6}$/12, –2$\sqrt{3}$/3, ±1),
 * ($\sqrt{10}$/4, –7$\sqrt{6}$/12, 5$\sqrt{3}$/6, ±1/2),
 * ($\sqrt{10}$/4, 3$\sqrt{6}$/4, 0, ±1),
 * ($\sqrt{3}$/4, 3$\sqrt{10}$/4, ±$\sqrt{6}$/2, ±1/2).

Much simpler coordinates can be given in five dimensions, as all permutations of:


 * (2$\sqrt{3}$, 3$\sqrt{10}$/2, $\sqrt{6}$, $\sqrt{10}$/2, 0).

Representations
A great prismatodecachoron has the following Coxeter diagrams:


 * x3x3x3x (full symmetry)
 * xxxux3xxuxx3xuxxx&#xt (A3 axial, truncated octahedron-first)