Swirlprismatodiminished rectified icositetrachoron

The swirlprismatodiminished rectified icositetrachoron is an isogonal polychoron with 24 chiral rectified triangular prisms, 24 triangular prisms, 24 triangular antiprisms and 72 vertices. Together with its dual, it is the first in an infinite family of small rhombitetratetrahedral swirlchora.

It can be constructed by removing an inscribed icositetrahedron of edge length $\sqrt{3}$ from a rectified icositetrachoron.

Vertex coordinates
Coordinates for the vertices of a swirlprismatodiminished rectified icositetrachoron of circumradius $\sqrt{3}$, centered at the origin, are given by:
 * ±($\sqrt{3}$/3, 0, $\sqrt{2}$, $\sqrt{2/3}$),
 * ±(-$\sqrt{3}$/6, ±1/2, $\sqrt{2}$, $\sqrt{2/3}$),
 * ±(0, 1, $\sqrt{2}$, 0),
 * ±(±$\sqrt{3}$/2, -1/2, $\sqrt{2}$, 0),
 * ±(-$\sqrt{3}$/3, 0, $\sqrt{2}$, -$\sqrt{2/3}$),
 * ±($\sqrt{3}$/6, ±1/2, $\sqrt{2}$, -$\sqrt{2/3}$),
 * ±(0, -1, $\sqrt{2}$/2, $\sqrt{6}$/2),
 * ±(±$\sqrt{3}$/2, 1/2, $\sqrt{2}$/2, $\sqrt{6}$/2),
 * ±($\sqrt{3}$/6, 3/2, $\sqrt{2}$/2, $\sqrt{6}$/6),
 * ±$\sqrt{3}$/6, -3/2, $\sqrt{2}$/2, $\sqrt{6}$/6),
 * ±(2$\sqrt{3}$/3, 1, $\sqrt{2}$/2, $\sqrt{6}$/6),
 * ±(2$\sqrt{3}$/3, -1, $\sqrt{2}$/2, $\sqrt{6}$/6),
 * ±(-5$\sqrt{3}$/6, 1/2, $\sqrt{2}$/2, $\sqrt{6}$/6),
 * ±(-5$\sqrt{3}$/6, -1/2, $\sqrt{2}$/2, $\sqrt{6}$/6),
 * ±(-$\sqrt{3}$/6, 3/2, $\sqrt{2}$/2, -$\sqrt{6}$/6),
 * ±{-$\sqrt{3}$/6, -3/2, $\sqrt{2}$/2, -$\sqrt{6}$/6),
 * ±(-2$\sqrt{3}$/3, 1, $\sqrt{2}$/2, -$\sqrt{6}$/6),
 * ±(-2$\sqrt{3}$/3, -1, $\sqrt{2}$/2, -$\sqrt{6}$/6),
 * ±(5$\sqrt{3}$/6, 1/2, $\sqrt{2}$/2, -$\sqrt{6}$/6),
 * ±(5$\sqrt{3}$/6, -1/2, $\sqrt{2}$/2, -$\sqrt{6}$/6),
 * ±(-$\sqrt{3}$/3, 0, 0, 2$\sqrt{6}$/3),
 * ±($\sqrt{3}$/6, ±1/2, 0, 2$\sqrt{6}$/3),
 * ±(-$\sqrt{3}$/6, 3/2, 0, $\sqrt{6}$/3),
 * ±{-$\sqrt{3}$/6, -3/2, 0, $\sqrt{6}$/3),
 * ±(-2$\sqrt{3}$/3, 1, 0, $\sqrt{6}$/3),
 * ±(-2$\sqrt{3}$/3, -1, 0, $\sqrt{6}$/3),
 * ±(5$\sqrt{3}$/6, 1/2, 0, $\sqrt{6}$/3),
 * ±(5$\sqrt{3}$/6, -1/2, 0, $\sqrt{6}$/3),
 * ±($\sqrt{3}$/6, 3/2, 0, -$\sqrt{6}$/3),
 * ±$\sqrt{3}$/6, -3/2, 0, -$\sqrt{6}$/3),
 * ±(2$\sqrt{3}$/3, 1, 0, -$\sqrt{6}$/3),
 * ±(2$\sqrt{3}$/3, -1, 0, -$\sqrt{6}$/3),
 * ±(-5$\sqrt{3}$/6, 1/2, 0, -$\sqrt{6}$/3),
 * ±(-5$\sqrt{3}$/6, -1/2, 0, -$\sqrt{6}$/3).

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
 * Rectangle (72): Swirlprismatodiminished rectified icositetrachoron
 * Isosceles triangle (144): Bi-icositetradiminished truncated icositetrachoron
 * Edge (72): Swirlprismatodiminished rectified icositetrachoron
 * Edge (144): Bi-icositetradiminished truncated icositetrachoron