Great rhombated tesseract

The great rhombated tesseract, or grit, also commonly called the cantitruncated tesseract, is a convex uniform polychoron that consists of 32 triangular prisms, 16 truncated tetrahedra, and 8 great rhombicuboctahedra. 1 triangular prism, 1 truncated tetrahedron, and 2 great rhombicuboctahedra join at each vertex. As one of its names suggests, it can be obtained by cantitruncating the tesseract.

Vertex coordinates
The vertices of a great rhombated tesseract of edge length 1 are given by all permutations of:


 * $$\left(±\frac{1+2\sqrt2}{2},\,±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$

Representations
A great rhombated tesseract has the following Coxeter diagrams:


 * x4x3x3o (full symmetry)
 * xxwwxx4xuxxux3xoooox&#xt (BC3 symmetry, great rhombicuboctahedron-first)
 * wx3xx3xw *b3oo&#zx (D4 symmetry)
 * Xwx xxw4xux3xoo&#zx (BC3×A1 symmetry)

Semi-uniform variant
The great rhombated tesseract has a semi-uniform variant of the form x4y3z3o that maintains its full symmetry. This variant uses 16 truncated tetrahedra of form y3z3o, 8 great rhombicuboctahedra of form x4y3z, and 32 triangular prisms of form x z3o as cells, with 3 edge lengths.

With edges of length a, b, and c (such that it forms a4b3c3o), its circumradius is given by $$\sqrt{\frac{2a^2+3b^2+2c^2+4bc+(3ab+2ac)\sqrt2}{2} }$$.

It has coordinates given by all permutations of:


 * $$\left(±\frac{a+(b+c)\sqrt2}{2},\,±\frac{a+(b+c)\sqrt2}{2},\,±\frac{a+b\sqrt2}{2},\,±\frac{a}{2}\right).$$