Swirlprismatodiminished rectified icositetrachoron

The swirlprismatodiminished rectified icositetrachoron or spidrico is an isogonal polychoron with 24 chiral rectified triangular prisms, 24 triangular prisms, 24 triangular antiprisms, and 72 vertices. 3 chiral rectified triangular prisms, 2 triangular antiprisms, and 2 triangular prisms join at each vertex. It can be constructed by removing the 24 vertices of an inscribed icositetrachoron of edge length $$\sqrt3$$ from a rectified icositetrachoron. In doing so the cuboctahedral cells have 3 vertices removed, while the cubes have 2 opposite corners removed and additional triangular prisms come in as the original's vertex figures.

The ratio between the longest and shortest edges is 1:$$\sqrt2$$ ≈ 1:1.41421.

Vertex coordinates
Coordinates for the vertices of a swirlprismatodiminished rectified icositetrachoron of circumradius $$\sqrt3$$, centered at the origin, are given by:
 * $$±\left(\frac{\sqrt3}{3},\,0,\,\sqrt2,\,\frac{\sqrt6}{3}\right),$$
 * $$±\left(-\frac{\sqrt3}{6},\,±\frac12,\,\sqrt2,\,\frac{\sqrt6}{3}\right),$$
 * $$±\left(0,\,1,\,\sqrt2,\,0\right),$$
 * $$±\left(±\frac{\sqrt3}{2},\,-\frac12,\,\sqrt2,\,0\right),$$
 * $$±\left(-\frac{\sqrt3}{3},\,0,\,\sqrt2,\,-\frac{\sqrt6}{3}\right),$$
 * $$±\left(\frac{\sqrt3}{6},\,±\frac12,\,\sqrt2,\,-\frac{\sqrt6}{3}\right),$$
 * $$±\left(0,\,-1,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{2}\right),$$
 * $$±\left(±\frac{\sqrt3}{2},\,\frac12,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{2}\right),$$
 * $$±\left(\frac{\sqrt3}{6},\,\frac32,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * ±\frac{\sqrt3}{6},\,-\frac32,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),
 * $$±\left(\frac{2\sqrt3}{3},\,1,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$±\left(\frac{2\sqrt3}{3},\,-1,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$±\left(-\frac{5\sqrt3}{6},\,\frac12,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$±\left(-\frac{5\sqrt3}{6},\,-\frac12,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$±\left(-\frac{\sqrt3}{6},\,\frac32,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * ±{-\frac{\sqrt3}{6},\,-\frac32,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),
 * $$±\left(-\frac{2\sqrt3}{3},\,1,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$±\left(-\frac{2\sqrt3}{3},\,-1,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$±\left(\frac{5\sqrt3}{6},\,\frac12,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$±\left(\frac{5\sqrt3}{6},\,-\frac12,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$±\left(-\frac{\sqrt3}{3},\,0,\,0,\,\frac{2\sqrt6}{3}\right),$$
 * $$±\left(\frac{\sqrt3}{6},\,±\frac12,\,0,\,\frac{2\sqrt6}{3}\right),$$
 * $$±\left(-\frac{\sqrt3}{6},\,\frac32,\,0,\,\frac{\sqrt6}{3}\right),$$
 * ±{-\frac{\sqrt3}{6},\,-\frac32,\,0,\,\frac{\sqrt6}{3}\right),
 * $$±\left(-\frac{2\sqrt3}{3},\,1,\,0,\,\frac{\sqrt6}{3}\right),$$
 * $$±\left(-\frac{2\sqrt3}{3},\,-1,\,0,\,\frac{\sqrt6}{3}\right),$$
 * $$±\left(\frac{5\sqrt3}{6},\,\frac12,\,0,\,\frac{\sqrt6}{3}\right),$$
 * $$±\left(\frac{5\sqrt3}{6},\,-\frac12,\,0,\,\frac{\sqrt6}{3}\right),$$
 * $$±\left(\frac{\sqrt3}{6},\,\frac32,\,0,\,-\frac{\sqrt6}{3}\right),$$
 * ±\frac{\sqrt3}{6},\,-\frac32,\,0,\,-\frac{\sqrt6}{3}\right),
 * $$±\left(\frac{2\sqrt3}{3},\,1,\,0,\,-\frac{\sqrt6}{3}\right),$$
 * $$±\left(\frac{2\sqrt3}{3},\,-1,\,0,\,-\frac{\sqrt6}{3}\right),$$
 * $$±\left(-\frac{5\sqrt3}{6},\,\frac12,\,0,\,-\frac{\sqrt6}{3}\right),$$
 * $$±\left(-\frac{5\sqrt3}{6},\,-\frac12,\,0,\,-\frac{\sqrt6}{3}\right).$$

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Chiral rectified triangular prism (24): Icositetrachoron
 * Triangular prism (24): Icositetrachoron
 * Triangular antiprism (24): Icositetrachoron
 * Triangle (24): Icositetrachoron
 * Edge (144): Non-uniform small prismatotetracontoctachoron