Disicositetratruncated disicositetrachoron

The disicositetratruncated disicositetrachoron, or ditdi, is a nonconvex uniform polychoron that consists of 24 truncated octahedra, 24 truncated cubes, 24 great cubicuboctahedra, and 24 cuboctatruncated cuboctahedra. 1 truncated cube, 1 truncated octahedron, 1 great cubicuboctahedron, and 2 cuboctatruncated cuboctahedra join at each vertex.

The disicositetratruncated disicositetrachoron contains the vertices of a tesseractihexadecatruncated prismatotesseractihexadecachoron.

Vertex coordinates
The vertices of a disicositetratruncated disicositetrachoron of edge length 1 are given by all permutations of:


 * $$\left(±\frac{2+\sqrt2}{2},\,±\sqrt2,\,±\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$$

The second set of vertices are identical to the vertices of an inscribed tesseractihexadecatruncated prismatotesseractihexadecachoron.

Related polychora
The disicositetratruncated disicositetrachoron is the colonel of a 3-member regiment that also includes the great tetrisicositetrachoron and great rhombic trisicositetrachoron.

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