Disicositetratruncated disicositetrachoron

Disicositetratruncated disicositetrachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Ditdi
Coxeter diagram	x3x4x3o4*a4/3*c ()
Elements
Cells	24 truncated octahedra, 24 truncated cubes, 24 great cubicuboctahedra, 24 cuboctatruncated cuboctahedra
Faces	192 triangles, 144 squares, 192 hexagons, 144 octagons, 144 octagrams
Edges	288+576+576
Vertices	576
Vertex figure	Isosceles trapezoidal pyramid, base edge lengths 1, √2–√2, √2, √2–√2; lateral edge lengths √3, √3, √2+√2, √2+√2
Measures (edge length 1)
Circumradius	${\sqrt {4+{\sqrt {2}}}}\approx 2.32685$
Hypervolume	$139+168{\sqrt {2}}\approx 376.58788$
Dichoral angles	Gocco–4–toe: 135°
	Tic–8–cotco: 135°
	Gocco–8/3–cotco: 135°
	Gocco–3–tic: 120°
	Toe–6–cotco: 120°
Related polytopes
Army	Semi-uniform Grico, edge lengths ${\sqrt {2}}-1$ (truncated cubes), 1 (sides of triangular prisms)
Regiment	Ditdi
Conjugate	Disicositetraquasitruncated disicositetrachoron
Abstract & topological properties
Flag count	18432
Euler characteristic	–144
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Tame

The disicositetratruncated disicositetrachoron, or ditdi, is a nonconvex uniform polychoron that consists of 24 truncated octahedra, 24 truncated cubes, 24 great cubicuboctahedra, and 24 cuboctatruncated cuboctahedra. 1 truncated cube, 1 truncated octahedron, 1 great cubicuboctahedron, and 2 cuboctatruncated cuboctahedra join at each vertex.

The disicositetratruncated disicositetrachoron contains the vertices of a tesseractihexadecatruncated prismatotesseractihexadecachoron.

Cross-sections

Vertex coordinates

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

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

The second set of vertices are identical to the vertices of an inscribed tesseractihexadecatruncated prismatotesseractihexadecachoron.

Related polychora

The disicositetratruncated disicositetrachoron is the colonel of a 3-member regiment that also includes the great tetrisicositetrachoron and great rhombic trisicositetrachoron.

External links=

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#412).

• Klitzing, Richard. "ditdi".