Sphenoverted tesseractitesseractihexadecachoron

The sphenoverted tesseractitesseractihexadecachoron, or wavitoth, is a nonconvex uniform polychoron that consists of 16 regular octahedra, 8 quasitruncated hexahedra, and 8 great cubicuboctahedra. 1 octahedron, 2 quasitruncated hexahedra, and 2 great cubicuboctahedra join at each vertex.

The sphenoverted tesseractitesseractihexadecachoron can be vertex-inscribed into a great distetracontoctachoron and contains the vertices of an octagrammic duoprism and the quasitruncated hexahedral prism.

Vertex coordinates
The vertices of a sphenoverted tesseractitesseractihexadecachoron of edge length 1 are given by all permutations of:
 * (±($\sqrt{2}$–1)/2, ±($\sqrt{2–√2}$–1)/2, ±1/2, ±1/2).