Rectified tesseract

The rectified tesseract, or rit, is a convex uniform polychoron that consists of 16 regular tetrahedra and 8 cuboctahedra. Two tetrahedra and three cuboctahedra join at each triangular prismatic vertex. As the name suggests, it can be obtained by rectifying the tesseract.

The rectified tesseract is the convex hull of two perpendicular bialternatosnub digonal-square duoprisms.

Vertex coordinates
The vertices of a rectified tesseract of edge length 1 are given by all permutations of:
 * (±$\sqrt{2}$/2, ±$\sqrt{6}$/2, ±$\sqrt{2}$/2, 0).

Alternatively, they can be given under D4 symmetry as even permutations of:


 * (±3$\sqrt{2}$/4, ±$\sqrt{2}$/4, ±$\sqrt{2}$/4, ±$\sqrt{2}$/4).