Small ditetrahedronary dishecatonicosachoron

Small ditetrahedronary dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Siddatady
Coxeter diagram	o3o3o5/3x5*b ()
Elements
Cells	120 dodecahedra, 120 ditrigonary dodecadodecahedra
Faces	1440 pentagons, 720 pentagrams
Edges	3600
Vertices	600
Vertex figure	Hypertruncated tetrahedron, edge lengths (1+√5)/2 (triangle edges) and (√5–1)/2 (other edges)
Edge figure	(doe 5 ditdid 5/2 ditdid 5)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825$
Hypervolume	$75\frac{11+5\sqrt5}{4} ≈ 415.88137$
Dichoral angles	Ditdid–5/2–ditdid: 144°
	Ditdid–5–doe: 36°
Central density	5
Number of external pieces	11160
Level of complexity	31
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Conjugate	Grand ditetrahedronary dishecatonicosachoron
Abstract & topological properties
Euler characteristic	–1080
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small ditetrahedronary dishecatonicosachoron, or siddatady, is a nonconvex uniform polychoron that consists of 120 regular dodecahedra and 120 ditrigonary dodecadodecahedra. 4 ditrigonary dodecadodecahedra and 4 dodecahedra 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" (#780).

• Klitzing, Richard. "siddatady".