# Icositetrafold octaswirlchoron

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Icositetrafold octaswirlchoron
200px
Rank4
TypeIsogonal
SpaceSpherical
Info
SymmetryBC3+×48, order 1152
Elements
Vertex figureEdge-vertical bisected square antitegum
Cells192 triangular antiprisms, 288 rhombic disphenoids
Faces192 triangles, 1152 scalene triangles
Edges144+288+576
Vertices144
Central density1
Euler characteristic0
Related polytopes
DualCubiswirlic hecatontetracontatetrachoron
Properties
ConvexYes
OrientableYes
NatureTame

The icositetrafold octaswirlchoron is an isogonal polychoron with 192 triangular antiprisms, 288 rhombic disphenoids and 144 vertices. It is the sixth in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1:$\frac{\sqrt{12+6\sqrt2+4\sqrt{9+6\sqrt2}}}{2}$ ≈ 1:3.05006.

## Vertex coordinates

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

• (0, 0, 0, 1),
• (1/2, 1/2, 1/2, 1/2),

defining an icositetrachoron, along with reflections through the x=y and z=w hyperplanes and with all sign changes of:

• (0, 0, 2/2, 2/2),
• (0, 2/2, 0, 2/2),
• (0, 2/2, 2/2, 0),
• (0, 0, 2-3/2, 2+3/2),
• (0, 0, 1/2, 3/2),

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

• ((3–1)/4, (3+1)/4, (3–1)/4, (3+1)/4),
• (2/4, 6/4, 2/4, 6/4),

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

• ((3-1)/4, (3+1)/4, (3+1)/4, (3-1)/4),
• (2/4, 6/4, 6/4, 2/4).

## Isogonal derivatives

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