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. It is the first in an infinite family of isogonal cuboctahedral swirlchora.

It can be constructed by removing an inscribed bitetracontoctachoron of edge length $$\sqrt{2+\sqrt2}$$ from a small prismatotetracontoctachoron.

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)/$\sqrt{2}$),