Icositetrafold cubiswirlchoron

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Icositetrafold cubiswirlchoron
200px
Rank4
TypeIsogonal
SpaceSpherical
Info
SymmetryBC3+×48, order 1152
Elements
Vertex figureEdge-vertical bisected triangular antitegum
Cells144 square antiprisms, 288 rhombic disphenoids
Faces144 squares, 1152 scalene triangles
Edges192+288+576
Vertices192
Central density1
Euler characteristic0
Related polytopes
DualOctaswirlic hecatonenneacontadichoron
Properties
ConvexYes
OrientableYes
NatureTame

The icositetrafold cubiswirlchoron is an isogonal polychoron with 144 square antiprisms, 288 rhombic disphenoids and 192 vertices. It is the second in an infinite family of isogonal cubic swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:2.49036.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of an icositetrafold cubiswirlchoron of circumradius 1, centered at the origin, are given by, along with their 90°, 180° and 270° rotations in the xy axis of:

  • ±(sin(kπ/12)/3+3, cos(kπ/12)/3+3, cos(kπ/12)/3-3, sin(kπ/12)/3-3),
  • ±(sin(kπ/12)/3-3, cos(kπ/12)/3-3, cos(kπ/12)/3+3, sin(kπ/12)/3+3),

where k is an integer from 0 to 11.

Isogonal derivatives[edit | edit source]

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