Truncated icosiheptaheptacontadipeton

The truncated icosiheptaheptacontadipeton or tojak, also called the truncated 221 polytope, is a convex uniform polypeton. It consists of 27 truncated triacontaditera, 27 demipenteracts, and 72 truncated hexatera. 5 truncated triacontaditera, 1 demipenteract, and 5 truncated hexatera join at each vertex. As the name suggests, it is the truncation of the icosiheptaheptacontadipeton.

Vertex coordinates
The vertices of a truncated icosiheptaheptacontadipeton of edge length $$2\sqrt2$$, centered at the origin, are given by all permutations and even sign changes of the first 5 coordinates of:
 * $$\left(1,\,1,\,1,\,1,\,1,\,3\sqrt3\right),$$
 * $$\left(2,\,2,\,2,\,2,\,2,\,2\sqrt3\right),$$
 * $$\left(3,\,3,\,3,\,1,\,1,\,\sqrt3\right),$$
 * $$\left(4,\,2,\,2,\,2,\,2,\,0\right),$$
 * $$\left(5,\,1,\,1,\,1,\,1,\,-\sqrt3\right),$$
 * $$\left(4,\,2,\,0,\,0,\,0,\,-2\sqrt3\right).$$