Frustosphenary dispenteractitriacontaditeron

The frustosphenary dispenteractitriacontaditeron, or fawdint, is a nonconvex uniform polyteron. It consists of 10 sphenoverted tesseractitesseractihexadecachora, 10 great tesseractitesseractihexadecachora, and 32 rectified pentachora. 3 sphenoverted tesseractitesseractihexadecachora, 2 great tesseractitesseractihexadecachora, and 1 rectified pentachoron join at each vertex.

The frustosphenary dispenteractitriacontaditeron contains the vertices of a sphenoverted tesseractitesseractihexadecachoric prism, square-quasitruncated hexahedral duoprism, octagrammic-great cubicuboctahedral duoprism, and octagrammic duoprismatic prism.

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

Related polytopes
The regiment of the frustosphenary dispenteractitriacontaditeron includes a total of 37 members plus one fissary member.