Truncated penteract

The truncated penteract, or tan, also called the truncated 5-cube, is a convex uniform polyteron. It consists of 32 regular pentachora and 10 truncated tesseracts. One pentachoron and 4 truncated tesseracts join at each vertex. As the name suggests, it is the truncation of the penteract.

Vertex coordinates
The vertices of a truncated penteract of edge length 1 are given by all permutations of:
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$

Representations
A truncated penteract has the following Coxeter diagrams:


 * x4x3o3o3o (full symmetry)
 * xwwx4xoox3oooo3oooo&#xt (BC4 axial, truncated tesseract-first)