Great cellated tesseractic tetracomb

The great cellated tesseractic tetracomb or gacotat, also called the omnitruncated tesseractic tetracomb is a convex uniform tetracomb. 2 great disprismatotesseractihexadecachora, 2 great rhombicuboctahedral prisms, and 1 octagonal duoprism join at each vertex of this tessellation. As the name suggests, it is the omnitruncation of the tesseractic tetracomb.

Vertex coordinates
The vertices of a great cellated tesseractic tetracomb of edge length 1 are given by all permutations of:


 * $$\left(±\frac12+(2+3\sqrt2)i,\,±\frac{1+\sqrt2}{2}+(2+3\sqrt2)j,\,±\frac{1+2\sqrt2}{2}+(2+3\sqrt2)k,\,±\frac{1+3\sqrt2}{2}+(2+3\sqrt2)l\right),$$

Where i, j, k, and l range over the integers.