Icosafold ambotetraswirlchoron

Icosafold ambotetraswirlchoron
File:Icosafold ambotetraswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	240+240 phyllic disphenoids, 80 triangular gyroprisms
Faces	480+480 scalene triangles, 240 isosceles triangles, 80 triangles
Edges	120+240+240+240
Vertices	120
Vertex figure	Polyhedroon with 4 tetragons and 16 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Rhombihexaswirlic hecatonicosachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A3●I2(20), order 480
Convex	Yes
Nature	Tame

The icosafold ambotetraswirlchoron is an isogonal polychoron with 80 triangular gyroprisms, 480 phyllic disphenoids of two kinds, and 120 vertices. 4 triangular gyroprisms and 16 phyllic disphenoids join at each vertex. It is the fifth in an infinite family of isogonal ambotetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:${\sqrt {\frac {{\sqrt {3}}+{\sqrt {5}}+{\sqrt {15}}+({\sqrt {3}}-1){\sqrt {10-2{\sqrt {5}}}}-15}{4{\sqrt {10+2{\sqrt {5}}}}-16}}}$ ≈ 1:2.63513.

Vertex coordinates

Coordinates for the vertices of an icosafold ambotetraswirlchoron of circumradius 1, centered at the origin, are given by, along with their 120° and 240° rotations in the xy axis of:

• ±(sin(kπ/10)/√3+√3, cos(kπ/10)/√3+√3, cos(kπ/10)/√3-√3, sin(kπ/10)/√3-√3),
• ±(sin((k+1)π/10)/√3-√3, cos((k+1)π/10)/√3-√3, -cos((k+1)π/10)/√3+√3, -sin((k+1)π/10)/√3+√3),

where k is an integer from 0 to 9.