Ditetrahedronary dishecatonicosachoron

Ditetrahedronary dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Dattady
Coxeter diagram	o3o3o3x5/2*b ()
Elements
Cells	120 great stellated dodecahedra, 120 small ditrigonary icosidodecahedra
Faces	1200 triangles, 1440 pentagrams
Edges	3600
Vertices	600
Vertex figure	Semi-uniform truncated tetrahedron, edge lengths (√5–1)/2 (triangle edges) and 1 (other edges)
Measures (edge length 1)
Circumradius	$\sqrt2 ≈ 1.41421$
Hypervolume	$5\frac{65+9\sqrt5}{4} ≈ 106.40576$
Dichoral angles	Sidtid–5/2–gissid: 144°
	Sidtid–3–sidtid: 120°
Central density	9
Number of external pieces	2520
Level of complexity	11
Related polytopes
Army	Hi, edge length $\frac{3-\sqrt5}{2}$
Regiment	Dattady
Conjugate	Great ditetrahedronary dishecatonicosachoron
Abstract & topological properties
Flag count	43200
Euler characteristic	–600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The ditetrahedronary dishecatonicosachoron, or dattady, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra and 120 small ditrigonary icosidodecahedra. 4 small ditrigonary icosidodecahedra and 4 great stellated dodecahedra join at each vertex, with a variant of the truncated tetrahedron as the vertex figure.

The ditetrahedronary dishecatonicosachoron contains the vertices and edges of a hexagonal duoprism, rhombidodecadodecahedral prism, and decachoron.

Cross-sections

Vertex coordinates

The vertices of a ditetrahedronary dishecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of:

• $\left(±1,\,±1,\,0,\,0\right),$
• $\left(±\frac{\sqrt5}{2},\,±\frac12,\,±\frac12,\,±\frac12\right),$
• $\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$
• $\left(±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4}\right),$

together with all the even permutations of:

• $\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±\frac{3-\sqrt5}{4},\,0\right),$
• $\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,0,\,±\frac{\sqrt5-1}{4}\right),$
• $\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±1,\,±\frac{\sqrt5-1}{4}\right).$

Related polychora

The ditetrahedronary dishecatonicosachoron is the colonel of a regiment with 37 members, plus four fissaries and two compounds, as well as a number of scaliform members.

External links

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#815).

• Bowers, Jonathan. "How to Make Dattady".

• Klitzing, Richard. "dattady".