Chiroicosioctafold cuboctaswirlchoron

Chiroicosioctafold cuboctaswirlchoron
Rank	4
Type	Isogonal
Elements
Cells	672+672+672 phyllic disphenoids, 336 rhombic disphenoids
Faces	1344+1344+1344 scalene triangles, 672 isosceles triangles
Edges	336+336+672+672+672
Vertices	336
Vertex figure	16-vertex polyhedron with 28 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Chirorhombidodecaswirlic triacositriacontahexachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3+●I2(28)×2R, order 1344
Convex	Yes
Nature	Tame

The chiroicosioctafold cuboctaswirlchoron is an isogonal polychoron with 336 rhombic disphenoids, 2016 phyllic disphenoids of three kinds, and 336 vertices. 4 rhombic disphenoids and 24 phyllic disphenoids join at each vertex. It is the fourth in an infinite family of isogonal chiral cuboctahedral swirlchora.

Vertex coordinates

Coordinates for the vertices of a chiroicosioctafold cuboctaswirlchoron of circumradius 1, centered at the origin, are given by, along with their 180° rotations in the xy axis and even sign changes of the first and third coordinates of:

• ±(sin(kπ/14)/√4+2√2, cos(kπ/14)/√4+2√2, cos(kπ/14)/√4-2√2, sin(kπ/14)/√4-2√2),
• ±(sin(kπ/14)/√4-2√2, cos(kπ/14)/√4-2√2, cos(kπ/14)/√4+2√2, sin(kπ/14)/√4+2√2),
• ±(cos((2k-1)π/28)/√4+2√2, -sin((2k-1)π/28)/√4+2√2, cos((2k-1)π/28)/√4-2√2, sin((2k-1)π/28)/√4-2√2),
• ±(cos((2k-1)π/28)/√4-2√2, -sin((2k-1)π/28)/√4-2√2, cos((2k-1)π/28)/√4+2√2, sin((2k-1)π/28)/√4+2√2),
• ±(sin((4k+9)π/56)/√2, cos((4k+9)π/56)/√2, cos((4k-9)π/56)/√2, sin((4k-9)π/56)/√2),

where k is an integer from 0 to 13.