Triacontadifold cuboctaswirlchoron

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Triacontadifold cuboctaswirlchoron
File:Triacontadifold cuboctaswirlchoron.png
Rank4
TypeIsogonal
Elements
Cells768+768 phyllic disphenoids, 192 square gyroprisms
Faces1536+1536 scalene triangles, 768 isosceles triangles, 192 squares
Edges384+768+768+768
Vertices384
Vertex figurePolyhedron with 4 tetragons and 16 triangles
Measures (edge length 1)
Central density1
Related polytopes
DualRhombidodecaswirlic triacosioctacontatetrachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB3●I2(32), order 1536
ConvexYes
NatureTame

The triacontadifold cuboctaswirlchoron is an isogonal polychoron with 192 square gyroprisms, 1536 phyllic disphenoids of two kinds, and 384 vertices. 4 square gyroprisms and 16 phyllic disphenoids join at each vertex. It is the fourth in an infinite family of isogonal cuboctahedral swirlchora.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a triacontadifold cuboctaswirlchoron 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/16)/4+22, cos(kπ/16)/4+22, cos(kπ/16)/4-22, sin(kπ/16)/4-22),
  • ±(sin(kπ/16)/4-22, cos(kπ/16)/4-22, cos(kπ/16)/4+22, sin(kπ/16)/4+22),
  • ±(sin((2k+4)π/32)/2, cos((2k+4)π/32)/2, cos((2k-4)π/32)/2, sin((2k-4)π/32)/2),

where k is an integer from 0 to 15.