# Bimesotruncatotetracontoctachoron

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Bimesotruncatotetracontoctachoron
Rank4
TypeIsogonal
Notation
Bowers style acronymBimtec
Coxeter diagramoo3ab4ba3oo&#zc
Elements
Cells144 ditetragonal trapezoprisms, 48 truncated cubes
Faces192 triangles, 576 isosceles trapezoids, 288 ditetragons
Edges288+576+576
Vertices576
Vertex figureNotch
Measures (for variant with trapezoids with 3 equal edges)
Edge lengthsShort base edges (576): 1
Lacing edges (288): 1
Long base edges (576): ${\displaystyle {\frac {4+{\sqrt {2}}}{2}}\approx 2.70711}$
Circumradius${\displaystyle {\sqrt {\frac {41+28{\sqrt {2}}}{2}}}\approx 6.34815}$
Central density1
Related polytopes
ArmyBimtec
RegimentBimtec
DualBimesoapiculatotetracontoctachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexYes
NatureTame

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 ${\displaystyle (b-a)(2-{\sqrt {2}})}$.

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