Small ditetrahedronary hexacosidishecatonicosachoron

Small ditetrahedronary hexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sidtaxady
Coxeter diagram	o3o3o3x5*a3/2*c ()
Elements
Cells	600 tetrahedra, 120 dodecahedra, 120 great ditrigonary icosidodecahedra
Faces	2400 triangles, 1440 pentagons
Edges	3600
Vertices	600
Vertex figure	Great tetradistetrahedron, edge lengths 1 and (1+√5)/2
Edge figure	(tet 3 gidtid 5 doe 5 gidtid 3)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825$
Hypervolume	$5\frac{265+112\sqrt5}{4} ≈ 644.29952$
Dichoral angles	Gidtid–5–doe: 36°
	Gidtid–3–tet: $\arccos\left(\frac{\sqrt{7+3\sqrt5}}{4}\right) ≈ 22.23876^\circ$
Central density	7
Number of external pieces	16920
Level of complexity	43
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Company	Sidtaxady
Conjugate	Grand retroditetrahedronary hexacosidishecatonicosachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small ditetrahedronary hexacosidishecatonicosachoron, or sidtaxady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, and 120 great ditrigonary icosidodecahedra. 4 dodecahedra, 4 tetrahedra, and 4 great ditrigonary 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" (#779).

• Klitzing, Richard. "sidtaxady".