Truncated small prismatotetracontoctachoron

The truncated small prismatotetracontoctachoron or tispic is a convex isogonal polychoron that consists of 48 truncated octahedra, 192 truncated triangular prisms, and 144 square antiprisms. 1 square antiprism, 1 truncated octahedron, and 3 truncated triangular prisms join at each vertex. It can be formed by truncating the small prismatotetracontoctachoron.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the prismatorhombated icositetrachoron, where if the prismatorhombated icositetrachora are of the form a3b4o3c, then c = a+2b. It is one of five polychora (including two transitional cases) formed from two prismatorhombated icositetrachora, and is the transitional point between the medial biprismatorhombatotetracontoctachoron and great biprismatorhombatotetracontoctachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt2$$ ≈ 1:1.41421. This variant uses regular hexagons as faces.

Vertex coordinates
The vertices of a truncated small prismatotetracontoctachoron of edge length 1, centered at the origin, are given by:


 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\sqrt2,\,±3\frac{2+\sqrt2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+3\sqrt2}{2},\,±\frac{5+3\sqrt2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac32,\,±3\frac{1+\sqrt2}{2},\,±3\frac{1+\sqrt2}{2}\right),$$
 * $$\left(±1,\,±1,\,±\frac{2+3\sqrt2}{2},\,±\frac{4+3\sqrt2}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{3+\sqrt2}{2},\,±\frac{3+2\sqrt2}{2},\,±3\frac{1+\sqrt2}{2}\right).$$