Chirohexafold diantiprismatoswirlchoron

Chirohexafold diantiprismatoswirlchoron
File:Chirohexafold diantiprismatoswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	24 rhombic disphenoids, 24 phyllic disphenoids, 48 irregular tetrahedra
Faces	24+24 isosceles triangles, 48+48+48 scalene triangles
Edges	24+24+24+48
Vertices	24
Vertex figure	10-vertex polyhedron with 16 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Chirodiantiprismatoswirlic icositetrachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2≀S2+/3, order 48
Convex	Yes
Nature	Tame

The chirohexafold diantiprismatoswirlchoron is an isogonal polychoron with 24 rhombic disphenoids, 24 phyllic disphenoids, 48 irregular tetrahedra, and 24 vertices. 4 rhombic disphenoids, 4 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It is the first in an infinite family of isogonal chiral digonal antiprismatic swirlchora.

The ratio between the longest and shortest edges is 1:${\sqrt {\frac {10-{\sqrt {5}}}{5}}}$ ≈ 1:1.24611.

Vertex coordinates

Coordinates for the vertices of a chirohexafold diantiprismatoswirlchoron of circumradius 1, centered at the origin, are given by, along with their 180° rotations in the xy axis of:

• ±(a*sin(kπ/3), a*cos(kπ/3), b*cos(kπ/3), b*sin(kπ/3)),
• ±(b*sin((k+1)π/3), b*cos((k+1)π/3), a*cos(kπ/3), a*sin(kπ/3)),

where a = 1/2, b = (1+√5)/4 and k is an integer from 0 to 2.