Icositetrafold octaswirlchoron

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Icositetrafold octaswirlchoron
File:Icositetrafold octaswirlchoron.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells288 rhombic disphenoids, 192 triangular gyroprisms
Faces1152 scalene triangles, 192 triangles
Edges144+288+576
Vertices144
Vertex figureEdge-vertical bisected square gyrotegum
Measures (circumradius 1)
Edge lengths8-valence (144):
 4-valence (288):
 3-valence (576):
Central density1
Related polytopes
DualCubiswirlic hecatontetracontatetrachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB3●I2(24), order 1152
ConvexYes
NatureTame

The icositetrafold octaswirlchoron is an isogonal polychoron with 192 triangular gyroprisms, 288 rhombic disphenoids, and 144 vertices. 8 triangular gyroprisms and 8 rhombic disphenoids join at each vertex. It is the sixth in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:3.05006.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of an icositetrafold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations of:

defining an icositetrachoron, along with all permutations of:

defining the dual icositetrachoron, along with reflections through the x=y and z=w hyperplanes of:

along with reflections through the x=y and z=w hyperplanes and with all even sign changes of:

along with reflections through the x=y and z=w hyperplanes and with all odd sign changes of:

Isogonal derivatives[edit | edit source]

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