Bimesotruncatotetracontoctachoron

Bimesotruncatotetracontoctachoron
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Bimtec
Coxeter diagram	oo3ab4ba3oo&#zc
Elements
Cells	144 ditetragonal trapezoprisms, 48 truncated cubes
Faces	192 triangles, 576 isosceles trapezoids, 288 ditetragons
Edges	288+576+576
Vertices	576
Vertex figure	Notch
Measures (for variant with trapezoids with 3 equal edges)
Edge lengths	Short base edges (576): 1
	Lacing edges (288): 1
	Long base edges (576): ${\frac {4+{\sqrt {2}}}{2}}\approx 2.70711$
Circumradius	${\sqrt {\frac {41+28{\sqrt {2}}}{2}}}\approx 6.34815$
Central density	1
Related polytopes
Army	Bimtec
Regiment	Bimtec
Dual	Bimesoapiculatotetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

The bimesotruncatotetracontoctachoron or bimtec is a convex isogonal polychoron that consists of 48 truncated cubes and 144 ditetragonal trapezoprisms. 2 truncated cubes and 4 ditetragonal trapezoprisms join at each vertex. It can be obtained as the convex hull of two opposite icositetricositetrachora (that is, variants of the tetracontoctachoron with F₄ symmetry).

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is $1:{\frac {4+{\sqrt {2}}}{2}}\approx 1:2.70711$.

External links

• Klitzing, Richard. "bimtec".