Chiroicosafold cuboctaswirlchoron

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Chiroicosafold cuboctaswirlchoron
File:Chiroicosafold cuboctaswirlchoron.png
Rank4
TypeIsogonal
Elements
Cells480+480+480 phyllic disphenoids, 240 rhombic disphenoids
Faces960+960+960 scalene triangles, 480 isosceles triangles
Edges240+240+480+480+480
Vertices240
Vertex figure16-vertex polyhedron with 28 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
DualChirorhombidodecaswirlic diacositetracontachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB3+●I2(20)×2R, order 960
ConvexYes
NatureTame

The chiroicosafold cuboctaswirlchoron is an isogonal polychoron with 240 rhombic disphenoids, 1440 phyllic disphenoids of three kinds, and 240 vertices. 4 rhombic disphenoids and 24 phyllic disphenoids join at each vertex. It is the third in an infinite family of isogonal chiral cuboctahedral swirlchora.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a chiroicosafold cuboctaswirlchoron of circumradius 1, centered at the origin, are given by, along with their 180° rotations in the xy axis and even sign changes of the first and third coordinates of::

  • ±(sin(kπ/10)/4+22, cos(kπ/10)/4+22, cos(kπ/10)/4-22, sin(kπ/10)/4-22),
  • ±(sin(kπ/10)/4-22, cos(kπ/10)/4-22, cos(kπ/10)/4+22, sin(kπ/10)/4+22),
  • ±(cos((2k-1)π/20)/4+22, -sin((2k-1)π/20)/4+22, cos((2k-1)π/20)/4-22, sin((2k-1)π/20)/4-22),
  • ±(cos((2k-1)π/20)/4-22, -sin((2k-1)π/20)/4-22, cos((2k-1)π/20)/4+22, sin((2k-1)π/20)/4+22),
  • ±(sin((4k+7)π/40)/2, cos((4k+7)π/40)/2, cos((4k-7)π/40)/2, sin((4k-7)π/40)/2),

where k is an integer from 0 to 9.