Biambotetracontoctachoron

The biambotetracontoctachoron or bamic is a convex isogonal polychoron that consists of 48 cubes and 144 square antiprisms. 2 cubes and 6 square antiprisms join at each vertex. It can be obtained as the convex hull of two oppositely oriented rectified icositetrachora.

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

The ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt2}{2}$$ ≈ 1:1.70711.

Vertex coordinates
The vertices of a biambotetracontoctachoron, derived from two perpendicular rectified icositetrachora of edge length 1, centered at the origin, are given by all permutations of:
 * $$\left(±1,,\,±1,\,±1,\,0\right),$$
 * $$\left(±\frac32,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0\right).$$