Small retroditetrahedronary hexacosidishecatonicosachoron

Small retroditetrahedronary hexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sirdtaxady
Coxeter diagram	x3o3/2o3o5*a ()
Elements
Cells	600 tetrahedra, 120 dodecahedra, 120 icosidodecahedra
Faces	2400 triangles, 1440 pentagons
Edges	3600
Vertices	600
Vertex figure	Quasirhombitetratetrahedron, edge lengths 1 and (1+√5)/2
Edge figure	(tet 3 id 5 doe 5 id 3)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825$
Hypervolume	$5\frac{405+194\sqrt5}{4} ≈ 1048.49648$
Dichoral angles	Id–3–tet: $\arccos\left(\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 82.23876°$
	Doe–5–id: 72°
Central density	14
Number of external pieces	161280
Level of complexity	316
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Company	Sidtaxady
Conjugate	Grand ditetrahedronary hexacosidishecatonicosachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small retroditetrahedronary hexacosidishecatonicosachoron, or sirdtaxady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, and 120 icosidodecahedra. 4 dodecahedra, 4 tetrahedra, and 6 icosidodecahedra join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#782).

• Klitzing, Richard. "sirdtaxady".