Icosioctafold octaswirlchoron

Icosioctafold octaswirlchoron
File:Icosioctafold octaswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	672+672 phyllic disphenoids
Faces	1344 scalene triangles 672+672 isosceles triangles
Edges	168+672+672
Vertices	168
Vertex figure	18-vertex polyhedron with 32 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Cubiswirlic hecatonhexacontoctachoron
Abstract & topological properties
Flag count	32256
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3●I2(28), order 1344
Flag orbits	24
Convex	Yes
Nature	Tame

The icosioctafold octaswirlchoron is an isogonal polychoron with 1344 phyllic disphenoids of two kinds and 168 vertices. 32 disphenoids join at each vertex. It is the seventh in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1:${\frac {\sqrt {2-{\sqrt {2}}\cos {\frac {3\pi }{28}}}}{2\sin {\frac {\pi }{28}}}}$ ≈ 1:3.64207.

Vertex coordinates

Coordinates for the vertices of an icosioctafold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations and sign changes of:

• ±(0, 0, sin(kπ/14), cos(kπ/14)),
• ±(sin(kπ/14), cos(kπ/14), 0, 0),

along with 90°, 180° and 270° rotations in the xy axis of:

• ±(sin((k+1/2)π/14)/√2, cos((k+1/2)π/14)/√2, cos((k+1/2)π/14)/√2, sin((k+1/2)π/14)/√2),

where k is an integer from 0 to 13.