Great octagonal spinoduoprism

The great octagonal spinoduoprism, or gondip, 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 quasidisprismatotesseractihexadecachora. Its vertex figure is in turn a blend of two vertex figures of the quasidisprismatotesseractihexadecachoron. It has the same symmetry as the octagonal duoprism.

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

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