Celligreatorhombated tesseractic tetracomb

The celligreatorhombated tesseractic tetracomb or cagratit, also called the stericantitruncated tesseractic tetracomb, is a convex uniform tetracomb. 1 great rhombated tesseract, 1 prismatorhombated tesseract, 1 small rhombicuboctahedral prism, 2 great rhombicuboctahedral prisms, and 1 square-octagonal duoprism join at each vertex of this tessellation. As the name suggests, it is the stericantitruncation of the tesseractic tetracomb.

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


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

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