Great discellidispenteractitriacontaditeron

The great discellidispenteractitriacontaditeron, or gidacadint, is a nonconvex uniform polyteron. It consists of 10 small skewverted prismatohexadecadisoctachora, 10 great cubihexadecadisoctachora, 32 prismatorhombated pentachora, 40 small rhombicuboctahedral prisms, and 40 quasitruncated cuboctahedral prisms. 1 small skewverted prismatohexadecadisoctachoron, 1 great cubihexadecadisoctachoron, 1 prismatorhombated pentachoron, 1 small rhombicuboctahedral prism, and 2 quasitruncated cuboctahedral prisms meet at each vertex.

The great discellidispenteractitriacontaditeron contains the vertices and edges of a tesseractihexadecaquasitruncated prismatotesseractihexadecachoric prism and octagonal-quasitruncated cuboctahedral duoprism.

Vertex coordinates
The vertices of a great discellidispenteractitriacontaditeron of edge length 1 are given by all permutations of:
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{2\sqrt2-1}{2},\,±\frac12,\,±\frac12\right).$$

Related polytopes
The great discellidispenteractitriacontaditeron is the colonel of a regiment that contains 15 members.