Octadecafold pyritocubiswirlchoron

Octadecafold pyritocubiswirlchoron
File:Octadecafold pyritocubiswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	432+432 phyllic disphenoids, 216 rhombic disphenoids
Faces	864+864 scalene triangles, 432 isosceles triangles
Edges	144+216+432+432
Vertices	144
Vertex figure	17-vertex polyhedron with 30 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Pyritooctaswirlic hecatontetracontatetrachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	(B3/2)●I2(18)×2R, order 864
Convex	Yes
Nature	Tame

The octadecafold pyritocubiswirlchoron is an isogonal polychoron with 216 rhombic disphenoids, 864 phyllic disphenoids of two kinds, and 144 vertices. 6 rhombic and 24 phyllic disphenoids join at each vertex. It is the third in an infinite family of isogonal pyritohedral cubic swirlchora.

The ratio between the longest and shortest edges is 1:${\sqrt {\frac {4+6\cos {\frac {\pi }{9}}}{1+2\sin {\frac {\pi }{18}}}}}$ ≈ 1:2.67464.

Vertex coordinates

Coordinates for the vertices of an octadecafold pyritocubiswirlchoron of circumradius 1, centered at the origin, are:

• ±(0, 0, sin(kπ/9), cos(kπ/9)),
• ±(sin(kπ/9), cos(kπ/9), 0, 0),

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

• ±(√6sin(kπ/9)/3, √6cos(kπ/9)/3, √3cos(kπ/9)/3, √3sin(kπ/9)/3),
• ±(√3cos(kπ/9)/3, √3sin(kπ/9)/3, -√6sin(kπ/9)/3, -√6cos(kπ/9)/3),

where k is an integer from 0 to 8.