Chirododecafold cuboctaswirlchoron

Chirododecafold cuboctaswirlchoron
File:Chirododecafold cuboctaswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	288 phyllic disphenoids, 144 rhombic disphenoids, 96 triangular gyroprisms
Faces	576+576 scalene triangles, 96 triangles
Edges	144+144+288+288
Vertices	144
Vertex figure	10-vertex polyhedron with 4 tetragons and 12 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Chirorhombidodecaswirlic hecatontetracontatetrachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3+●I2(12)×2R, order 576
Convex	Yes
Nature	Tame

The chirododecafold cuboctaswirlchoron is an isogonal polychoron with 96 triangular gyroprisms, 144 rhombic disphenoids, 288 phyllic disphenoids, and 144 vertices. 4 triangular gyroprisms, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It is the second in an infinite family of isogonal chiral cuboctahedral swirlchora.

The ratio between the longest and shortest edges is 1:${\sqrt {4-2{\sqrt {2}}+{\sqrt {18+12{\sqrt {2}}}}}}$ ≈ 1:1.47858.

Vertex coordinates

Coordinates for the vertices of a chirododecafold 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/6)/√4+2√2, cos(kπ/6)/√4+2√2, cos(kπ/6)/√4-2√2, sin(kπ/6)/√4-2√2),
• ±(sin(kπ/6)/√4-2√2, cos(kπ/6)/√4-2√2, cos(kπ/6)/√4+2√2, sin(kπ/6)/√4+2√2),
• ±(cos((2k-1)π/12)/√4+2√2, -sin((2k-1)π/12)/√4+2√2, cos((2k-1)π/12)/√4-2√2, sin((2k-1)π/12)/√4-2√2),
• ±(cos((2k-1)π/12)/√4-2√2, -sin((2k-1)π/12)/√4-2√2, cos((2k-1)π/12)/√4+2√2, sin((2k-1)π/12)/√4+2√2),
• ±(sin((4k+5)π/24)/√2, cos((4k+5)π/24)/√2, cos((4k-3)π/24)/√2, sin((4k-3)π/24)/√2),

where k is an integer from 0 to 5.