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

Related polychora
The sphenoverted tesseractitesseractihexadecachoron is the colonel of a 7-member regiment. Its other members include the quasirhombated tesseract, great rhombic disoctachoron, great pseudorhombic prismatotesseract, grand quasirhombic prismatotesseract, disprismatointercepted tesseractihexadecachoron, and prismatointercepted tesseractitesseractihexadecachoron.