Icositetrafold octaswirlchoron

Icositetrafold octaswirlchoron
200px (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Info
Symmetry	BC3+×48, order 1152
Elements
Vertex figure	Edge-vertical bisected square antitegum
Cells	192 triangular antiprisms, 288 rhombic disphenoids
Faces	192 triangles, 1152 scalene triangles
Edges	144+288+576
Vertices	144
Central density	1
Euler characteristic	0
Related polytopes
Dual	Cubiswirlic hecatontetracontatetrachoron
Properties
Convex	Yes
Orientable	Yes
Nature	Tame

The icositetrafold octaswirlchoron is an isogonal polychoron with 192 triangular antiprisms, 288 rhombic disphenoids and 144 vertices. It is the sixth in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1:$\frac{\sqrt{12+6\sqrt2+4\sqrt{9+6\sqrt2}}}{2}$ ≈ 1:3.05006.

Vertex coordinates

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

• (0, 0, 0, 1),
• (1/2, 1/2, 1/2, 1/2),

defining an icositetrachoron, along with reflections through the x=y and z=w hyperplanes and with all sign changes of:

• (0, 0, √2/2, √2/2),
• (0, √2/2, 0, √2/2),
• (0, √2/2, √2/2, 0),
• (0, 0, √2-√3/2, √2+√3/2),
• (0, 0, 1/2, √3/2),

along with reflections through the x=y and z=w hyperplanes and with all even sign changes of:

• ((√3–1)/4, (√3+1)/4, (√3–1)/4, (√3+1)/4),
• (√2/4, √6/4, √2/4, √6/4),

along with reflections through the x=y and z=w hyperplanes and with all odd sign changes of:

• ((√3-1)/4, (√3+1)/4, (√3+1)/4, (√3-1)/4),
• (√2/4, √6/4, √6/4, √2/4).

Isogonal derivatives

Substitution by vertices of these following elements will produce these convex isogonal polychora:

• Triangular antiprism (192): Icositetrafold cubiswirlchoron
• Triangle (192): Icositetrafold cubiswirlchoron
• Edge (144): Icositetrafold octaswirlchoron