Disprismatotesseract

The diprismatotesseract, or dippit, is a nonconvex uniform polychoron that consists of 32 triangular prisms, 24 cubes, and 8 small cubicuboctahedra. Three triangular prisms, three cubes, and three small cubicuboctahedra join at each vertex.

It also has 8 cubes and 16 tetrahedra as pseudofacets.

Vertex coordinates
Its vertices are the same as those of its regiment colonel, the small disprismatotesseractihexadecachoron.