# Biprismatotetracontoctachoron

Biprismatotetracontoctachoron
Rank4
TypeIsogonal
Notation
Bowers style acronymBipec
Coxeter diagramab3oo4oo3ba&#zc
Elements
Cells48 octahedra, 192 triangular prisms, 288 rectangular trapezoprisms
Faces384 triangles, 576 isosceles trapezoids, 576 rectangles
Edges144+576+576
Vertices288
Vertex figureTriakis square pyramid
Measures (for variant with trapezoids with 3 equal edges)
Edge lengthsShort base edges (576): 1
Lacing edges (144): 1
Long base edges (576): $1+{\sqrt {\frac {2+{\sqrt {2}}}{2}}}\approx 2.30656$ Circumradius${\sqrt {\frac {6+3{\sqrt {2}}+2{\sqrt {2+{\sqrt {2}}}}+2{\sqrt {4+2{\sqrt {2}}}}}{2}}}\approx 3.09551$ Central density1
Related polytopes
ArmyBipec
RegimentBipec
DualBicrystallotetracontoctachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexYes
NatureTame

The biprismatotetracontoctachoron or bipec is a convex isogonal polychoron that consists of 48 octahedra, 288 rectangular trapezoprisms and 192 triangular prisms. 1 octahedron, 4 triangular prisms, and 4 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two opposite small disprismatoicositetricositetrachora (that is, variants of the small prismatotetracontoctachoron with F4 symmetry).

If the small disprismatoicositetricositetrachora have edge lengths a and b, the lacing edges between then have length $(b-a){\sqrt {2-{\sqrt {2}}}}$ .

Using the ratio method, the lowest possible ratio between the longest and shortest edges is $1:1+{\sqrt {\frac {2+{\sqrt {2}}}{2}}}\approx 1:2.30656$ .