Octafold ambotetraswirlchoron

Octafold ambotetraswirlchoron
File:Octafold ambotetraswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	96 phyllic disphenoids, 32 triangular gyroprisms
Faces	192 scalene triangles, 96 isosceles triangles, 32 triangles
Edges	48+96+96
Vertices	48
Vertex figure	Polyhedron with 4 tetragons and 8 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Rhombihexaswirlic tetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A3●I2(8), order 192
Convex	Yes
Nature	Tame

The octafold ambotetraswirlchoron is an isogonal polychoron with 32 triangular gyroprisms, 96 phyllic disphenoids, and 48 vertices. 4 triangular gyroprisms and 8 phyllic disphenoids join at each vertex. It is the second in an infinite family of isogonal ambotetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:${\frac {\sqrt {8+4{\sqrt {2}}-2{\sqrt {9+6{\sqrt {2}}}}}}{2}}$ ≈ 1:1.15041.

Vertex coordinates

Coordinates for the vertices of an octafold ambotetraswirlchoron of circumradius 1, centered at the origin, are given by, along with their 120° and 240° rotations in the xy axis of:

• ±(sin(kπ/4)/√3+√3, cos(kπ/4)/√3+√3, cos(kπ/4)/√3-√3, sin(kπ/4)/√3-√3),
• ±(sin((k+1)π/4)/√3-√3, cos((k+1)π/4)/√3-√3, -cos((k+1)π/4)/√3+√3, -sin((k+1)π/4)/√3+√3),

where k is an integer from 0 to 3.