Great biprismatorhombatotetracontoctachoron

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Great biprismatorhombatotetracontoctachoron
Rank4
TypeIsogonal
Notation
Bowers style acronymGabiparc
Coxeter diagramac3bo4ob3ca&#zd (c > a+2b)
Elements
Cells576 wedges, 288 rectangular trapezoprisms, 144 square antiprisms, 192 ditrigonal prisms, 48 truncated octahedra
Faces1152 isosceles triangles, 288 squares, 576+576 rectangles, 1152 isosceles trapezoids, 384 ditrigons
Edges576+1152+1152+1152
Vertices1152
Vertex figureParatriakis isosceles trapezoidal pyramid
Measures (edge length 1)
Central density1
Related polytopes
ArmyGabiparc
RegimentGabiparc
DualGreat bicrystallorthotetracontoctachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexYes
NatureTame

The great biprismatorhombatotetracontoctachoron or gabiparc is a convex isogonal polychoron that consists of 48 truncated tetrahedra, 192 ditrigonal prisms, 144 square antiprisms, 288 rectangular trapezoprisms, and 576 wedges. 1 truncated octahedron, 2 ditrigonal prisms, 1 square antiprism, 2 rectangular trapezoprisms, and 3 wedges join at each vertex.

[It is one of a total of five distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite prismatorhombated icositetrachora. In this case, if the prismatorhombated icositetrachora are of the form a3b4o3c, then c must be greater than a+2b (producing the truncated small prismatotetracontoctachoron in the limiting case). The lacing edges generally have length .