Teriprismated hexeract

The teriprismated hexeract or tapox, also called the penticantellated hexacontatetrapeton or penticantellated 6-orthoplex, is a convex uniform polypeton. It consists of 12 small prismated penteracts, 64 small rhombated hexatera, 60 small disprismatotesseractihexadecachoric prisms, 192 small rhombated pentachoric prisms, 240 square-cuboctahedral duoprisms, and 160 triangular-cubic duoprisms. 1 small prismated penteract, 1 small rhombated hexateron, 2 small disprismatotesseractihexadecachoric prisms, 3 small rhombated pentachoric prisms, 3 square-cuboctahedral duoprisms, and 1 triangular-cubic duoprism join at each vertex. As the name suggests, it is the penticantellation of the hexacontatetrapeton.

Coordinates
The vertex coordinates of a small birhombated hexeract, centered at the origin and with unit edge length, are given by all permutations of:
 * $$\left(±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,±\frac12\right).$$