Retroditetrahedronary trishecatonicosachoron

Retroditetrahedronary trishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Radatathi
Coxeter diagram	o3o3o5x5/3*a ()
Elements
Cells	120 dodecahedra, 120 great stellated dodecahedra, 120 dodecadodecahedra
Faces	1440 pentagons, 1440 pentagrams
Edges	3600
Vertices	600
Vertex figure	Quasirhombitetratetrahedron, edge lengths (√5–1)/2 and (1+√5)/2
Measures (edge length 1)
Circumradius	$\sqrt2 \approx 1.41421$
Hypervolume	$\frac{375}{2} = 187.5$
Dichoral angles	Doe–5–did: 144°
	Gissid–5/2–did: 72°
Central density	65
Number of external pieces	45720
Level of complexity	105
Related polytopes
Army	Hi
Regiment	Dattady
Company	Dattathi
Conjugate	Retroditetrahedronary dishecatonicosachoron
Abstract & topological properties
Euler characteristic	–480
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The retroditetrahedronary trishecatonicosachoron, or radatathi, is a nonconvex uniform polychoron that consists of 120 regular dodecahedra, 120 great stellated dodecahedra, and 120 dodecadodecahedra. 4 great stellated dodecahedra, 4 dodecahedra, and 6 dodecadodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the ditetrahedronary dishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#819).

• Klitzing, Richard. "radatathi".