Biprismatotetracontoctachoron

Biprismatotetracontoctachoron
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Bipec
Coxeter diagram	ab3oo4oo3ba&#zc
Elements
Cells	48 octahedra, 192 triangular prisms, 288 rectangular trapezoprisms
Faces	384 triangles, 576 isosceles trapezoids, 576 rectangles
Edges	144+576+576
Vertices	288
Vertex figure	Triakis square pyramid
Measures (for variant with trapezoids with 3 equal edges)
Edge lengths	Short 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 density	1
Related polytopes
Army	Bipec
Regiment	Bipec
Dual	Bicrystallotetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

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 $1:1+{\sqrt {\frac {2+{\sqrt {2}}}{2}}}\approx 1:2.30656$.

External links

• Klitzing, Richard. "bipec".