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.

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.

It can also be formed as the convex hlul of two oppositely-oriented semi-uniform variants of the prismatorhombated icositetrachoron of the form a3b4o3c, where if a = 1, then c = b+2.

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


 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\sqrt2,\,±3\frac{2+\sqrt2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+3\sqrt2}{2},\,±\frac{5+3\sqrt2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac32,\,±3\frac{1+\sqrt2}{2},\,±3\frac{1+\sqt2}{2}\right),$$
 * $$\left(±1,\,±1,\,±\frac{2+3\sqrt2}{2},\,±\frac{4+3\sqrt2}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{3+\sqrt2}{2},\,±\frac{3+2\sqrt2}{2},\,±3\frac{1+\sqrt2}{2}\right).$$

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