Icosidifold tetraswirlchoron

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Icosidifold tetraswirlchoron
File:Icosidifold tetraswirlchoron.png
Rank4
TypeIsogonal
Elements
Cells264+264+264 phyllic disphenoids
Faces528+528 scalene triangles, 264+264 isosceles triangles
Edges88+264+264+264
Vertices88
Vertex figure20-vertex polyhedron with 30 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
DualTetraswirlic octacontoctachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA3●I2(22), order 528
ConvexYes
NatureTame

The icosidifold tetraswirlchoron is an isogonal polychoron with 792 phyllic disphenoids of three kinds and 88 vertices. 36 disphenoids join at each vertex. It is the eleventh in an infinite family of isogonal tetrahedral swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:3.73032.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of an icosidifold tetraswirlchoron of circumradius 1, centered at the origin, are given by:

  • ±(0, 0, sin(kπ/11), cos(kπ/11)),

along with 120° and 240° rotations in the xy axis of:

  • ±(6sin(kπ/11)/3, 6cos(kπ/11)/3, 3cos(kπ/11)/3, 3sin(kπ/11)/3),

where k is an integer from 0 to 10.