Cubic transitional biomnitruncatotetracontoctachoron

The cubic transitional biomnitruncatotetracontoctachoron or catbotic, also known as the octahedral transitional biomnitruncatotetracontoctachoron, is a convex isogonal polychoron that consists of 48 orthoaligned ditruncated cubes, 192 ditrigonal prisms, and 288 rectangular trapezoprisms. 2 orthoaligned ditruncated cubes, 1 ditrigonal prism, and 1 rectangular trapezoprism 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 great rhombicuboctahedra a3b4c and b4c3d have the same circumradius, which happens if d = $$a+\frac{\sqrt2}{3}b-\frac{\sqrt2}{3}c$$. 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 cubic transitional omnisnub bitetracontoctachoron, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt{4-2\sqrt2}}{2}$$ ≈ 1:1.54120.