# Biambotetracontoctachoron

Biambotetracontoctachoron
Rank4
TypeIsogonal
Notation
Bowers style acronymBamic
Coxeter diagramoo3xo4ox3oo&#zy
Elements
Cells48 cubes, 144 square antiprisms
Faces576 isosceles triangles, 288 squares
Edges288+576 = 864
Vertices192
Vertex figureTriangular bifrustum
Measures (based on two rectified icositetrachora of edge length 1)
Edge lengthsLacing edges (288): ${\displaystyle 2-{\sqrt {2}}\approx 0.58579}$
Edges of rectified icositetrachora (576): 1
Circumradius${\displaystyle {\sqrt {3}}\approx 1.73205}$
Central density1
Related polytopes
ArmyBamic
RegimentBamic
DualBijungatotetracontoctachoron
Abstract & topological properties
Flag count11520
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexYes
NatureTame

The biambotetracontoctachoron or bamic is a convex isogonal polychoron that consists of 48 cubes and 144 square antiprisms. 2 cubes and 6 square antiprisms join at each vertex. It can be obtained as the convex hull of two oppositely oriented rectified icositetrachora.

The biambotetracontoctachoron contains the vertices of a square-octagonal prismantiprismoid and the square double prismantiprismoid.

The ratio between the longest and shortest edges is ${\displaystyle 1:{\frac {2+{\sqrt {2}}}{2}}\approx 1:1.70711}$

## Vertex coordinates

The vertices of a biambotetracontoctachoron are derived from two perpendicular rectified icositetrachora of edge length 1, centered at the origin, are given by all permutations of:

• ${\displaystyle \left(\pm 1,\,\pm 1,\,\pm 1,\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {3}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\sqrt {2}},\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,0\right)}$.