Tesseractihemioctachoron

The tesseractihemioctachoron, or tho, is a uniform hemipolychoron. It has 8 regular tetrahedra and 4 central octahedra as cells, with 4 tetrahedra and 3 octahedra at each vertex in the form of a tetrahemihexahedron. It is the 4D demicross.

It is a faceting of the hexadecachoron, analogous to how the tetrahemihexahedron is a faceting of the octahedron. It shares the hexadecachoron's vertices, edges, and faces. The 8 tetrahedra are half of those of the hexadecachoron, while the octahedra are its original vertex figures.

Notably, as well as being isogonal, the tesseractihemioctachoron is also edge and face-transitive. It is one of only four non-regular uniform polychora to be vertex, edge, and face transitive.

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