# Bitetracontoctachoron

Bitetracontoctachoron
Rank4
TypeNoble
Notation
Bowers style acronymBicont
Coxeter diagramo3m4m3o ()
Elements
Cells288 tetragonal disphenoids
Faces576 isosceles triangles
Edges144+192
Vertices48
Vertex figureTriakis octahedron
Measures (based on two icositetrachora of edge length 1)
Edge lengthsLacing edges (144): ${\displaystyle {\sqrt {2-{\sqrt {2}}}}\approx 0.76537}$
Edges of icositetrachora (192): 1
Inradius${\displaystyle {\frac {2+{\sqrt {2}}}{4}}\approx 0.85355}$
Dichoral angle${\displaystyle \arccos \left(-{\frac {1+2{\sqrt {2}}}{4}}\right)\approx 163.15788^{\circ }}$
Central density1
Related polytopes
ArmyBicont
RegimentBicont
DualTetracontoctachoron
ConjugateGreat bitetracontoctachoron
Abstract & topological properties
Flag count6912
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexYes
NatureTame

The bitetracontoctachoron or bicont, also known as the tetradisphenoidal diacosioctacontoctachoron or octafold octaswirlchoron, is a convex noble polychoron with 288 tetragonal disphenoids as cells. 24 cells join at each vertex, with the vertex figure being a triakis octahedron. It can be constructed as the convex hull of 2 dual icositetrachora.

It is the second in an infinite family of isogonal octahedral swirlchora (the octafold octaswirlchoron) and the first in an infinite family of isogonal chiral cuboctahedral swirlchora.

The ratio between the longest and shortest edges is 1:${\displaystyle {\sqrt {\frac {2+{\sqrt {2}}}{2}}}}$ ≈ 1:1.30656.

The tetragonal disphenoid cells of this polychoron are similar to those used as the vertex figure of the great tetracontoctachoron.

## Vertex coordinates

Coordinates for the vertices of a bitetracontoctachoron of circumradius 1, centered at the origin, are given by all permutations of:

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

## Variations

The bitetracontoctachoron has a number of isogonal or isotopic variations:

## Isogonal derivatives

Substitution by vertices of these following elements will produce these convex isogonal polychora: