Ditetrahedronary dishecatonicosachoron

Ditetrahedronary dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
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	${\sqrt {2}}\approx 1.41421$
Hypervolume	$5{\frac {65+9{\sqrt {5}}}{4}}\approx 106.40576$
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 ${\frac {3-{\sqrt {5}}}{2}}$
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:

• $\left(\pm 1,\,\pm 1,\,0,\,0\right),$
• $\left(\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}}\right),$

together with all the even permutations of:

• $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,0\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {\sqrt {5}}{2}},\,0,\,\pm {\frac {{\sqrt {5}}-1}{4}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {{\sqrt {5}}-1}{4}}\right).$

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".