Distetracontoctachoron

Distetracontoctachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Doc
Coxeter diagram	x3x4x3x4/3*a ()
Elements
Cells	48 great rhombicuboctahedra, 48 quasitruncated cuboctahedra
Faces	576 squares, 384 hexagons, 144 octagons, 144 octagrams
Edges	1152+1152
Vertices	1152
Vertex figure	Phyllic disphenoid, edge lengths √2 (2), √3 (2), √2+√2 (1), and √2–√2 (1)
Measures (edge length 1)
Circumradius	${\sqrt {6}}\approx 2.44949$
Hypervolume	456
Dichoral angles	Quitco–8/3–quitco: 135°
	Girco–6–quitco: 120°
	Girco–4–quitco: 90°
	Girco–8–girco: 45°
Number of external pieces	9120
Level of complexity	197
Related polytopes
Army	Semi-uniform Gippic, edge lengths ${\sqrt {2}}-1$ (octagons), $2-{\sqrt {2}}$ (remaining edges)
Regiment	Doc
Conjugate	Distetracontoctachoron
Convex core	Tetracontoctachoron
Abstract & topological properties
Flag count	27648
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

The distetracontoctachoron, or doc, is a nonconvex uniform polychoron that consists of 48 great rhombicuboctahedra and 48 quasitruncated cuboctahedra. 2 of each join at each vertex.

Gallery

• 

  Vertices and edges

• 

  Cross-sections

Vertex coordinates

The vertices of a distetracontoctachoron of edge length 1 are given by all permutations of:

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

External links

• Bowers, Jonathan. "Category 9: Omnitruncates" (#348).

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

• Klitzing, Richard. "doc".