Prismatic transitional biomnitruncatotetracontoctachoron

The prismatic transitional biomnitruncatotetracontoctachoron or petbotic is a convex isogonal polychoron that consists of 48 great rhombicuboctahedra, 144 ditetragonal trapezoprisms, and 192 orthoaligned truncated triangular prisms. 1 reat rhombicuboctahedron, 1 ditetragnal trapezoprism, and 2 orthoaligned truncated triangular prisms join at each vertex.

It is one of a total of four distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite great disprismatoicositetricositetrachora (that is, variants of the great prismatotetracontoctachoron with single F4 symmetry). If the great disprismatoicositetricositetrachora are of the form a3b4c3d, then this form occurs when the ditrigonal prisms a c3d and a3b d have the same circumradius, which happens if d = a+b/2-c/2. The lacing edges generally have length $$\sqrt{(2-\sqrt2)(a-d)^2+(6-4\sqrt2)(b-c)^2+(6-4\sqrt2)(a-d)(b-c)}$$.

This polychoron can be alternated into a prismatic transitional omnisnub bitetracontoctachoron, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt2}{2}$$ ≈ 1:1.70711.