Enneacontahexadiminished small prismatodemihexeract

The enneacontahexadiminished small prismatodemihexeract, or nadsophax, is a convex scaliform polypeton. It consists of 12 rectified tesseractic alterprisms, 12 rectified tesseractic prisms, 32 tridiminished rectified hexatera, 32 hexadiminished small prismated hexatera, and 64 triangular-tetrahedral duoprisms.

Just as the small prismatodemihexeract can be created by alternating the small cellated hexeract (with some minor edge length adjustments), the enneacontahexadiminished small prismatodemihexeract is an alternation of the hecatonenneacontadidiminished small cellated hexeract.

Vertex coordinates
The vertices of an enneacontahexadiminished small prismatodemihexeract of edge length 1 are given by even sign changes and all permutations of the first two, second two, and/or last two coordinates of:

$$\biggl(\frac{\sqrt2}{4},\frac{\sqrt2}{4},\frac{3\sqrt2}{4},\frac{\sqrt2}{4},\frac{3\sqrt2}{4},\frac{\sqrt2}{4}\biggr),$$

$$\biggl(\frac{3\sqrt2}{4},\frac{\sqrt2}{4},\frac{\sqrt2}{4},\frac{\sqrt2}{4},\frac{3\sqrt2}{4},\frac{\sqrt2}{4}\biggr),$$

$$\biggl(\frac{3\sqrt2}{4},\frac{\sqrt2}{4},\frac{3\sqrt2}{4},\frac{\sqrt2}{4},\frac{\sqrt2}{4},\frac{\sqrt2}{4}\biggr).$$