Octafold cuboctaswirlchoron

The octafold cuboctaswirlchoron, also known as the swirlprismatodiminished small prismatotetracontoctachoron, is an isogonal polychoron with 48 square antiprisms, 192 phyllic disphenoids, and 96 vertices. 4 square antiprisms and 8 phyllic disphenoids join at each vertex. It is the first in an infinite family of isogonal cuboctahedral swirlchora.

It can be constructed by removing the vertices of an inscribed bitetracontoctachoron of edge length $$\sqrt{2+\sqrt2}$$ from a small prismatotetracontoctachoron. The antiprism cells are the vertex figures of the small prismatotetracontoctachoron. The disphenoids are formed by removing 2 vertices from the triangular prism cells.

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

Vertex coordinates
Coordinates for the vertices of an octafold cuboctaswirlchoron of circumradius 1, centered at the origin, are given by, along with their 90°, 180° and 270° rotations in the xy axis of: where k is an integer from 0 to 3.
 * ±(sin(kπ/4)/$\sqrt{4+2√2}$, cos(kπ/4)/$\sqrt{4+2√2}$, cos(kπ/4)/$\sqrt{4-2√2}$, sin(kπ/4)/$\sqrt{4-2√2}$),
 * ±(sin(kπ/4)/$\sqrt{4-2√2}$, cos(kπ/4)/$\sqrt{4-2√2}$, cos(kπ/4)/$\sqrt{4+2√2}$, sin(kπ/4)/$\sqrt{4+2√2}$),
 * ±(sin((2k+1)π/8)/$\sqrt{2}$, cos((2k+1)π/8)/$\sqrt{2}$, cos((2k-1)π/8)/$\sqrt{2}$, sin((2k-1)π/8)/$\sqrt{2}$),