Bitruncatotetracontoctachoron

The bitruncatotetracontoctachoron or bitec is a convex isogonal polychoron that consists of 48 cubes, 144 square antiprisms, 288 tetragonal disphenoids and 576 digonal disphenoids obtained as the convex hull of two opposite truncated icositetrachora.

The bitruncatotetracontoctachoron contains the vertices of a square-octagonal prismantiprismoid and the square double prismantiprismoid.

Vertex coordinates
The vertices of a bitruncatotetracontoctachoron, assuming that the square antiprisms are uniform of edge length 1, centered at the origin, are given by all permutations of:
 * (0, ±$\sqrt{2}$/2, ±(1+$\sqrt{1+√2}$)/2, ±(1+$\sqrt{2}$+$\sqrt{1+√2}$)/2),
 * (±1/2, ±1/2, ±1/2, ±(1+$\sqrt{2}$+$\sqrt{2+2√2}$)/2),
 * (±($\sqrt{2}$+$\sqrt{2+2√2}$-2)/4, ±(2+$\sqrt{2}$+$\sqrt{2+2√2}$)/4, ±(2+$\sqrt{2}$+$\sqrt{2+2√2}$)/4), ±(2+$\sqrt{2}$+$\sqrt{2+2√2}$)/4),
 * (±($\sqrt{2}$+$\sqrt{2+2√2}$)/4, ±($\sqrt{2}$+$\sqrt{2+2√2}$)/4, ±($\sqrt{2}$+$\sqrt{2+2√2}$)/4), ±(4+$\sqrt{2}$+$\sqrt{2+2√2}$)/4).

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by all permutations of:
 * (0, ±$\sqrt{2}$/2, ±$\sqrt{2}$, ±3$\sqrt{2}$/2),
 * (±1/2, ±1/2, ±1/2, ±5/2),
 * (±1/2, ±3/2, ±3/2, ±3/2),
 * (±1, ±1, ±1, ±2).