Tetragonal-antiwedge difold tritetraswirlchoron

Tetragonal-antiwedge difold tritetraswirlchoron
File:Tetragonal-antiwedge difold tritetraswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	24 phyllic disphenoids, 24 tetragonal antiwedges
Faces	24+24 isosceles triangles, 48 scalene triangles, 24 isosceles trapezoids
Edges	24+24+24+24
Vertices	24
Vertex figure	Digonal-rectangular notch
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Tetragonal-antiwedge intersected tritetraswirlic icositetrachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A3+×4, order 48
Convex	Yes
Nature	Tame

The tetragonal-antiwedge difold tritetraswirlchoron is a convex isogonal polychoron that consists of 24 tetragonal antiwedges and 24 phyllic disphenoids. 6 tetragonal antiwedges and 4 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of three hexadecachora or two orthogonal 12-5 step prisms.

The ratio between the longest and shortest edges is 1:$\sqrt{2+\sqrt2}$ ≈ 1:1.84776.

Vertex coordinates

Coordinates for the vertices of a tetragonal-antiwedge difold tritetraswirlchoron are given by:

• (a*sin(2πk/12), a*cos(2πk/12), b*sin(10πk/12), b*cos(10πk/12)),
• (b*sin(2πk/12), b*cos(2πk/12), a*sin(10πk/12), a*cos(10πk/12)),

where a = √18-6√3/6, b = √18+6√3/6 and k is an integer from 0 to 11.

External links

• Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".