Octagonal spinoduoprism

The octagonal spinoduoprism, or ondip, is a nonconvex uniform polychoron that consists of 64 regular tetrahedra, 128 triangular prisms, and 64 cubes. 2 tetrahedra, 6 triangular prisms, and 4 cubes join at each vertex.

It was discovered in March 2006, constructed as a blend of 4 small disprismatotesseractihexadecachora. Its vertex figure is in turn a blend of two vertex figures of the small disprismatotesseractihexadecachoron. It has the same symmetry as the octagonal duoprism.

Vertex coordinates
The vertices of an octagonal spinoduoprism of edge length 1 are given by all permutations of the first two and/or last two coordinates of:
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$

Related polychora
The regiment of the octagonal spinoduoprism contains one other uniform member (the small ditetragonal spinoduoprism), a fissary uniform member (the small ditetragonal fissary duoprism, and 10 scaliform members.