Hexadecafold cuboctaswirlchoron

Hexadecafold cuboctaswirlchoron
File:Hexadecafold cuboctaswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	384 phyllic disphenoids, 96 square gyroprisms
Faces	768 scalene triangles, 384 isosceles triangles, 96 squares
Edges	192+384+384
Vertices	192
Vertex figure	Polyhedron with 4 tetragons and 8 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Rhombidodecaswirlic hecatonenneacontadichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3●I2(16), order 768
Convex	Yes
Nature	Tame

The hexadecafold cuboctaswirlchoron is an isogonal polychoron with 96 square gyroprisms, 384 phyllic disphenoids, and 192 vertices. 4 square gyroprisms and 8 phyllic disphenoids join at each vertex. It is the second in an infinite family of isogonal cuboctahedral swirlchora.

The ratio between the longest and shortest edges is 1:${\frac {\sqrt {6+2{\sqrt {4-2{\sqrt {2}}}}}}{2}}$ ≈ 1:1.42870.

Vertex coordinates

Coordinates for the vertices of a hexadecafold cuboctaswirlchoron of circumradius 1, centered at the origin, are given by, along with their 90°, 180° and 270° rotations in the xy axis of:

• ±(sin(kπ/8)/√4+2√2, cos(kπ/8)/√4+2√2, cos(kπ/8)/√4-2√2, sin(kπ/8)/√4-2√2),
• ±(sin(kπ/8)/√4-2√2, cos(kπ/8)/√4-2√2, cos(kπ/8)/√4+2√2, sin(kπ/8)/√4+2√2),
• ±(sin((2k+2)π/16)/√2, cos((2k+2)π/16)/√2, cos((2k-2)π/16)/√2, sin((2k-2)π/16)/√2),

where k is an integer from 0 to 7.