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 a snub decachoron, 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)