Octadecafold tetraswirlchoron

Octadecafold tetraswirlchoron
File:Octadecafold tetraswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	216 phyllic disphenoids, 72 triangular gyroprisms
Faces	432 scalene triangles, 216 isosceles triangles, 72 triangles
Edges	72+216+216
Vertices	72
Vertex figure	14-vertex polyhedron with 6 tetragons and 12 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Tetraswirlic heptacontadichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A3●I2(18), order 432
Convex	Yes
Nature	Tame

The octadecafold tetraswirlchoron is an isogonal polychoron with 72 triangular gyroprisms, 216 phyllic disphenoids, and 72 vertices. 6 triangular gyroprisms and 12 phyllic disphenoids join at each vetex. It is the ninth in an infinite family of isogonal tetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:${\frac {\csc {\frac {\pi }{18}}}{2}}$ ≈ 1:2.87939.

Vertex coordinates

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

• ±(0, 0, sin(kπ/9), cos(kπ/9)),

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),

where k is an integer from 0 to 8.