Pentacontafold icosaswirlchoron

Pentacontafold icosaswirlchoron
Rank	4
Type	Isogonal
Elements
Cells	3000+3000 phyllic disphenoids
Faces	6000 scalene triangles, 3000+3000 isosceles triangles
Edges	600+3000+3000
Vertices	600
Vertex figure	Alternate-metatriakis decagonal tegum
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Dodecaswirlic hexacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H3●I2(50), order 6000
Convex	Yes
Nature	Tame

The pentacontafold icosaswirlchoron is an isogonal polychoron with 6000 tetragonal disphenoids of two kinds and 600 vertices. 40 disphenoids join at each vertex. It is the fifth in an infinite family of isogonal icosahedral swirlchora.

Vertex coordinates

Coordinates for the vertices of a pentacontafold icosaswirlchoron of circumradius 1, centered at the origin, are given by:

• ±(0, 0, sin(kπ/25), cos(kπ/25)),
• ±(cos(kπ/25), sin(kπ/25), 0, 0),

along with 72°, 144°, 216° and 288° rotations in the xy axis of:

• ±(2sin(kπ/25)/√10+2√5, 2cos(kπ/25)/√10+2√5, 2cos(kπ/25)/√10-2√5, 2sin(kπ/25)/√10-2√5),
• ±(2sin(kπ/25)/√10-2√5, 2cos(kπ/25)/√10-2√5, -2cos(kπ/25)/√10+2√5, -2sin(kπ/25)/√10+2√5),

where k is an integer from 0 to 24.