Dodecafold triantiprismatoswirlchoron

Dodecafold triantiprismatoswirlchoron
(OFF file)
Rank	4
Type	Isogonal
Elements
Cells	144 irregular tetrahedra, 72+72 phyllic disphenoids, 24 triangular gyroprisms
Faces	144+144+144+144 scalene triangles, 72 isosceles triangles, 24 triangles
Edges	72+72+72+72+144
Vertices	72
Vertex figure	Polyhedron with 2 tetragons and 16 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Triantitegmatoswirlic heptacontadichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	((G2×A1)/2)●I2(12), order 144
Convex	Yes
Nature	Tame

The dodecafold triantiprismatoswirlchoron is an isogonal polychoron with 24 triangular gyroprisms, 144 phyllic disphenoids of two kinds, 144 irregular tetrahedra, and 72 vertices. 2 triangular gyroprisms, 8 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It is the second in an infinite family of isogonal triangular antiprismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\frac {\sqrt {14+7{\sqrt {3}}-{\sqrt {119+68{\sqrt {3}}}}}}{2}}$ ≈ 1:1.63835.

Vertex coordinates

Coordinates for the vertices of a dodecafold triantiprismatoswirlchoron, centered at the origin, are given by, along with their 120° and 240° rotations in the xy axis of:

• ±(a*sin(kπ/6), a*cos(kπ/6), b*cos(kπ/6), b*sin(kπ/6)),
• ±(b*sin((k+2)π/6), b*cos((k+2)π/6), a*cos(kπ/6), a*sin(kπ/6)),

where a = √3/3, b = √78+18√17/12 and k is an integer from 0 to 5.