Tetracontoctafold cubiswirlchoron

Tetracontoctafold cubiswirlchoron
File:Tetracontoctafold cubiswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	1152 phyllic disphenoids, 576 rhombic disphenoids, 288 square gyroprisms
Faces	2304+2304 scalene triangles, 288 squares
Edges	384+576+1152+1152
Vertices	384
Vertex figure	17-vertex polyhedron with 6 tetragons and 18 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Octaswirlic triacosioctacontatetrachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3●I2(48), order 2304
Convex	Yes
Nature	Tame

The tetracontoctafold cubiswirlchoron is an isogonal polychoron with 288 square gyroprisms, 576 rhombic disphenoids, 1152 phyllic disphenoids, and 384 vertices. 6 square gyroprisms, 6 rhombic disphenoids, and 12 phyllic disphenoids join at each vertex. It is the fourth in an infinite family of isogonal cubic swirlchora.

The ratio between the longest and shortest edges is 1:${\sqrt {\frac {3-{\sqrt {3}}}{6-3{\sqrt {2+{\sqrt {2+{\sqrt {3}}}}}}}}}$ ≈ 1:4.97006.

Vertex coordinates

Coordinates for the vertices of an tetracontoctafold cubiswirlchoron of circumradius 1, centered at the origin, are given by (along with their 90°, 180° and 270° rotations in the xy axis):

• $\left({\frac {\sin \left(k\pi /24\right)}{\sqrt {3+{\sqrt {3}}}}},\,{\frac {\cos \left(k\pi /24\right)}{\sqrt {3+{\sqrt {3}}}}},\,{\frac {\cos \left(k\pi /24\right)}{\sqrt {3-{\sqrt {3}}}}},\,{\frac {\sin \left(k\pi /24\right)}{\sqrt {3-{\sqrt {3}}}}}\right),$
• $\left({\frac {\sin \left(k\pi /24\right)}{\sqrt {3-{\sqrt {3}}}}},\,{\frac {\cos \left(k\pi /24\right)}{\sqrt {3-{\sqrt {3}}}}},\,{\frac {\cos \left(k\pi /24\right)}{\sqrt {3+{\sqrt {3}}}}},\,{\frac {\sin \left(k\pi /24\right)}{\sqrt {3+{\sqrt {3}}}}}\right),$

where k is an integer from 0 to 23.