Swirlprismatodiminished rectified hexacosichoron

The swirlprismatodiminished rectified hexacosichoron, or spidrox,, is a convex scaliform polychoron. It consists of 120 pentagonal prisms, 120 pentagonal antiprisms, and 600 square pyramids. Together with its dual, it is the first in an infinite family of icosidodecahedral swirlchora.

It can be constructed by diminishing the rectified hexacosichoron, specifically by removing the 120 vertices of an inscribed hexacosichoron. As a result every icosahedral cell of the rectified hexacosichoron gets diminished down to a pentagonal antiprism, while every octahedral cell gets diminished down to a square pyramid. The pentagonal prism cells are the vertex figures under the removed vertices.

Vertex coordinates
A swirlprismatodiminished rectified hexacosichoron of edge length 1 has vertex coordinates given by:
 * (0, 0, ±(1+$\sqrt{2}$)/2, ±(3+$\sqrt{5}$)/2)
 * (0, 0, ±(3+$\sqrt{5+2√5}$)/2, ±(1+$\sqrt{5}$)/2)
 * (0, ±(1+$\sqrt{(5+2√5)/10}$)/2, 0, ±(3+$\sqrt{5}$)/2)
 * (0, –(1+$\sqrt{7+3√5}$)/2, –(3+$\sqrt{5}$)/2, 0)
 * (0, (1+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/2, 0)
 * (0, ±(3+$\sqrt{5}$)/2, 0, ±(1+$\sqrt{5}$)/2)
 * (0, –(3+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/2, 0)
 * (0, (3+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/2, 0)
 * (–(1+$\sqrt{5}$)/2, 0, 0, (3+$\sqrt{5}$)/2)
 * ((1+$\sqrt{5}$)/2, 0, 0, –(3+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, 0, ±(3+$\sqrt{5}$)/2, 0)
 * (±(1+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2, 0, 0)
 * (–(3+$\sqrt{5}$)/2, 0, 0, –(1+$\sqrt{5}$)/2)
 * ((3+$\sqrt{5}$)/2, 0, 0, (1+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/2, 0, ±(1+$\sqrt{5}$)/2, 0)
 * (±(3+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/2, 0, 0)
 * (0, –1/2, –(1+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4)
 * (0, 1/2, (1+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4)
 * (0, ±(1+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±1/2)
 * (0, ±(5+3$\sqrt{5}$)/4, ±1/2, ±(1+$\sqrt{5}$)/4)
 * (–1/2, 0, ±(5+3$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4)
 * (1/2, 0, ±(5+3$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/4, 0, ±(5+3$\sqrt{5}$)/4)
 * (±1/2, ±(5+3$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, 0)
 * (±(1+$\sqrt{5}$)/4), 0, ±1/2, ±(5+3$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4), ±1/2, ±(5+3$\sqrt{5}$)/4, 0)
 * (–(1+$\sqrt{5}$)/4), ±(5+3$\sqrt{5}$)/4, 0, –1/2)
 * ((1+$\sqrt{5}$)/4), ±(5+3$\sqrt{5}$)/4, 0, 1/2)
 * (±(5+3$\sqrt{5}$)/4, 0, ±(1+$\sqrt{5}$)/4, ±1/2)
 * (±(5+3$\sqrt{5}$)/4, ±1/2, 0, ±(1+$\sqrt{5}$)/4)
 * (±(5+3$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, 1/2, 0)
 * (±(5+3$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, –1/2, 0)
 * (0, –(3+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4)
 * (0, (3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4)
 * (0, ±(5+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2)
 * (0, ±(2+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4)
 * (–(3+$\sqrt{5}$)/4, 0, ±(5+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2)
 * ((3+$\sqrt{5}$)/4, 0, ±(5+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2, 0)
 * (±(3+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2, 0, ±(5+$\sqrt{5}$)/4)
 * (±(5+$\sqrt{5}$)/4, 0, ±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4)
 * (±(5+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4, 0, ±(2+$\sqrt{5}$)/2)
 * (±(5+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, 0)
 * (±(5+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, 0)
 * (±(2+$\sqrt{5}$)/2, 0, ±(3+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4, 0)
 * (–(2+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4, 0, –(3+$\sqrt{5}$)/4)
 * ((2+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4, 0, (3+$\sqrt{5}$)/4)
 * (–1/2, –1/2, ±(2+$\sqrt{5}$)/2, –(2+$\sqrt{5}$)/2)
 * (–1/2, 1/2, –(2+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2)
 * (–1/2, 1/2, (2+$\sqrt{5}$)/2, –(2+$\sqrt{5}$)/2)
 * (1/2, ±1/2, –(2+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (1/2, –1/2, (2+$\sqrt{5}$)/2, –(2+$\sqrt{5}$)/2)
 * (1/2, 1/2, –(2+$\sqrt{5}$)/2, –(2+$\sqrt{5}$)/2)
 * (1/2, 1/2, (2+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (±1/2, –(2+$\sqrt{5}$)/2, –1/2, ±(2+$\sqrt{5}$)/2)
 * (±1/2, (2+$\sqrt{5}$)/2, 1/2, (2+$\sqrt{5}$)/2)
 * (–1/2, ±(2+$\sqrt{5}$)/2, 1/2, –(2+$\sqrt{5}$)/2)
 * (–1/2, (2+$\sqrt{5}$)/2, –1/2, –(2+$\sqrt{5}$)/2)
 * (1/2, –(2+$\sqrt{5}$)/2, 1/2, (2+$\sqrt{5}$)/2)
 * (1/2, (2+$\sqrt{5}$)/2, –1/2, (2+$\sqrt{5}$)/2)
 * (1/2, (2+$\sqrt{5}$)/2, 1/2, –(2+$\sqrt{5}$)/2)
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2, ±1/2)
 * (±(2+$\sqrt{5}$)/2, ±1/2, ±1/2, ±(2+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, –1/2, (2+$\sqrt{5}$)/2, –1/2)
 * (–(2+$\sqrt{5}$)/2, –1/2, ±(2+$\sqrt{5}$)/2, 1/2)
 * (–(2+$\sqrt{5}$)/2, 1/2, –(2+$\sqrt{5}$)/2, ±1/2)
 * (–(2+$\sqrt{5}$)/2, 1/2, (2+$\sqrt{5}$)/2, 1/2)
 * ((2+$\sqrt{5}$)/2, ±1/2, –(2+$\sqrt{5}$)/2, –1/2)
 * ((2+$\sqrt{5}$)/2, –1/2, (2+$\sqrt{5}$)/2, 1/2)
 * ((2+$\sqrt{5}$)/2, 1/2, –(2+$\sqrt{5}$)/2, 1/2)
 * ((2+$\sqrt{5}$)/2, 1/2, (2+$\sqrt{5}$)/2, –1/2)
 * (±(2+$\sqrt{5}$)/2, –(2+$\sqrt{5}$)/2, –1/2, ±1/2)
 * (±(2+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2, 1/2, –1/2)
 * (–(2+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2, 1/2, 1/2)
 * (–(2+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2, –1/2, 1/2)
 * ((2+$\sqrt{5}$)/2, –(2+$\sqrt{5}$)/2, 1/2, –1/2)
 * ((2+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2, –1/2, –1/2)
 * ((2+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2, 1/2, 1/2)
 * (±1/2, ±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4)
 * (±1/2, –(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/2)
 * (–1/2, –(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2)
 * (–1/2, (3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (–1/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2)
 * (1/2, ±(3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/2)
 * (1/2, –(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2)
 * (1/2, (3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2)
 * (1/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/2)
 * (±1/2, –(3+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4)
 * (±1/2, (3+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4)
 * (–1/2, ±(3+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4)
 * (–1/2, (3+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4)
 * (1/2, –(3+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4)
 * (1/2, (3+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4)
 * (1/2, (3+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4), ±1/2, ±(3+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4), –(3+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2, 1/2)
 * (–(1+$\sqrt{5}$)/4), –(3+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, –1/2)
 * (–(1+$\sqrt{5}$)/4), (3+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/2, ±1/2)
 * (–(1+$\sqrt{5}$)/4), (3+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2, –1/2)
 * ((1+$\sqrt{5}$)/4), ±(3+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/2, 1/2)
 * ((1+$\sqrt{5}$)/4), –(3+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2, –1/2)
 * ((1+$\sqrt{5}$)/4), (3+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/2, –1/2)
 * ((1+$\sqrt{5}$)/4), (3+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2, 1/2)
 * (±(1+$\sqrt{5}$)/4), –(3+$\sqrt{5}$)/2, 1/2, –(3+$\sqrt{5}$)/4)
 * (–(1+$\sqrt{5}$)/4), –(3+$\sqrt{5}$)/2, ±1/2, (3+$\sqrt{5}$)/4)
 * (–(1+$\sqrt{5}$)/4), (3+$\sqrt{5}$)/2, –1/2, ±(3+$\sqrt{5}$)/4)
 * (–(1+$\sqrt{5}$)/4), (3+$\sqrt{5}$)/2, 1/2, (3+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/4), ±(3+$\sqrt{5}$)/2, –1/2, –(3+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/4), –(3+$\sqrt{5}$)/2, 1/2, (3+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/4), (3+$\sqrt{5}$)/2, –1/2, (3+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/4), (3+$\sqrt{5}$)/2, 1/2, –(3+$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/4, –1/2, –(3+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/4, 1/2, (3+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4)
 * (–(3+$\sqrt{5}$)/4, ±1/2, (3+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4)
 * (–(3+$\sqrt{5}$)/4, 1/2, –(3+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4)
 * ((3+$\sqrt{5}$)/4, –1/2, (3+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4)
 * ((3+$\sqrt{5}$)/4, 1/2, –(3+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4)
 * ((3+$\sqrt{5}$)/4, 1/2, (3+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, 1/2, (3+$\sqrt{5}$)/2)
 * (–(3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, ±1/2, –(3+$\sqrt{5}$)/2)
 * (–(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, –1/2, ±(3+$\sqrt{5}$)/2)
 * (–(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, 1/2, –(3+$\sqrt{5}$)/2)
 * ((3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, –1/2, (3+$\sqrt{5}$)/2)
 * ((3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, 1/2, –(3+$\sqrt{5}$)/2)
 * ((3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, –1/2, –(3+$\sqrt{5}$)/2)
 * ((3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, 1/2, (3+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4, ±1/2)
 * (±(3+$\sqrt{5}$)/2, –1/2, –(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/2, 1/2, (1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4)
 * (–(3+$\sqrt{5}$)/2, ±1/2, (1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4)
 * (–(3+$\sqrt{5}$)/2, 1/2, –(1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4)
 * ((3+$\sqrt{5}$)/2, –1/2, (1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4)
 * ((3+$\sqrt{5}$)/2, 1/2, –(1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4)
 * ((3+$\sqrt{5}$)/2, 1/2, (1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4, ±1/2)
 * (±(3+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4, 1/2)
 * (–(3+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4, –1/2)
 * (–(3+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4, –1/2)
 * ((3+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4, 1/2)
 * ((3+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4, 1/2)
 * ((3+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4, –1/2)
 * (±(3+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4, ±1/2, ±(1+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4), ±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4), –(1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4)
 * (–(1+$\sqrt{5}$)/4), –(1+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4)
 * (–(1+$\sqrt{5}$)/4), (1+$\sqrt{5}$)/2, –(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4)
 * (–(1+$\sqrt{5}$)/4), (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/4), ±(1+$\sqrt{5}$)/2, –(2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/4), –(1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/4), (1+$\sqrt{5}$)/2, –(2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/4), (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4), –(2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * (–(1+$\sqrt{5}$)/4), –(2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2)
 * (–(1+$\sqrt{5}$)/4), (2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2)
 * (–(1+$\sqrt{5}$)/4), (2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2)
 * ((1+$\sqrt{5}$)/4), ±(2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * ((1+$\sqrt{5}$)/4), –(2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2)
 * ((1+$\sqrt{5}$)/4), (2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2)
 * ((1+$\sqrt{5}$)/4), (2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2)
 * (–(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2)
 * (–(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2)
 * ((3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2)
 * ((3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2)
 * ((3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4)
 * (±(3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4)
 * (–(3+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4)
 * (–(3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4)
 * ((3+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4)
 * ((3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4)
 * ((3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2)
 * (–(1+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2)
 * (–(1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2)
 * ((1+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2)
 * ((1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2)
 * ((1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4)
 * (–(1+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4)
 * (–(1+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, –(2+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4)
 * ((1+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, (2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4)
 * (–(2+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4)
 * (–(2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4)
 * (–(2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4)
 * ((2+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4)
 * ((2+$\sqrt{5}$)/2, –(1+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4)
 * ((2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4)
 * ((2+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2)
 * (–(2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * (–(2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/2)
 * (–(2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * ((2+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2)
 * ((2+$\sqrt{5}$)/2, –(3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * ((2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * ((2+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/4, –(1+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4)

These are derived by removing 120 vertices from the rectified hexacosichoron.