Prismatic transitional biomnitruncatotetracontoctachoron

Prismatic transitional biomnitruncatotetracontoctachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Petbotic
Coxeter diagram	ad3bc4cb3da&#ze (d = a+b/2-c/2)
Elements
Cells	144 ditetragonal trapezoprisms, 192 orthoaligned truncated triangular prisms, 48 great rhombicuboctahedra
Faces	1152 isosceles trapezoids, 576 rectangles, 384 ditrigons, 288+288 ditetragons
Edges	1152+1152+1152+1152
Vertices	2304
Vertex figure	Irregular tetrahedron
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Prismatic transitional intersected biomnistellatotetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

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 ${\sqrt {(2-{\sqrt {2}})(a-d)^{2}+(6-4{\sqrt {2}})(b-c)^{2}+(6-4{\sqrt {2}})(a-d)(b-c)}}$.

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:${\frac {2+{\sqrt {2}}}{2}}$ ≈ 1:1.70711.