Prismatic transitional biomnitruncatotetracontoctachoron

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Prismatic transitional biomnitruncatotetracontoctachoron
Bowers style acronymPetbotic
Coxeter diagramad3bc4cb3da&#ze (d = a+b/2-c/2)
Cells144 ditetragonal trapezoprisms, 192 orthoaligned truncated triangular prisms, 48 great rhombicuboctahedra
Faces1152 isosceles trapezoids, 576 rectangles, 384 ditrigons, 288+288 ditetragons
Vertex figureIrregular tetrahedron
Measures (edge length 1)
Central density1
Related polytopes
DualPrismatic transitional intersected biomnistellatotetracontoctachoron
Abstract & topological properties
Euler characteristic0
SymmetryF4×2, order 2304

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 .

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: ≈ 1:1.70711.