Great terated hexeract

The great terated hexeract or gotaxog, also called the pentisteriruncicantituncated dodecapeton, pentisteriruncicantituncated 6-cube, or omnitruncated 6-cube, is a convex uniform polypeton. It consists of 12 great cellated penteracts, 64 great cellidodecatera, 192 great prismatodecachoric prisms, 60 great disprismatotesseractihexadecachoric prisms, 240 octagonal-truncated octahedral duoprisms, and 160 hexagonal-great rhombicuboctahedral duoprisms. 1 great cellated penteract, 1 great cellidodecateron, 1 great prismatodecachoric prism, 1 great disprismatotesseractihexadecachoric prism, 1 octagonal-truncated octahedral duoprism, and 1 hexagonal-great rhombicuboctahedral duoprism join at each vertex. As the name suggests, it is the omnitruncation of the hexeract.

Coordinates
The vertex coordinates of a great terated hexeract, centered at the origin and with unit edge length, are given by all permutations of:
 * $$\left(±\frac{1+5\sqrt2}{2},\,±\frac{1+4\sqrt2}{2},\,±\frac{1+3\sqrt2}{2},\,±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$