Great cellidodecateron

The great cellidodecateron, or gocad, also called the great cellated hexateron or omnitruncated 5-simplex, is a convex uniform polyteron. It consists of 20 hexagonal duoprisms, 30 truncated octahedral prisms, and 12 great prismatodecachora. 2 great prismatodecachora, 2 truncated octahedral prisms, and 1 hexagonal duoprism join at each vertex. As the name suggests, it is the omnitruncate of the A5 family.

This polyteron can be alternated into a snub dodecateron, but that cannot be made uniform.

It is the 6th-order permutohedron.

Vertex coordinates
The vertices of a great cellidodecateron of edge length 1 can be given in 6 dimensions as all permutations of:
 * $$\left(\frac{5\sqrt2}{2},\,2\sqrt2,\,\frac{3\sqrt2}{2},\,\sqrt2,\,\frac{\sqrt2}{2},\,0\right).$$