Dispenteractibitruncated triacontaditeron

Dispenteractibitruncated triacontaditeron
(OFF file)
Rank	5
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Danbitot
Coxeter diagram	o3x3x3o *b4/3x4*c ()
Elements
Tera	32 decachora, 10 tesseractihexadecatruncated tesseractihexadecachora, 10 tesseractihexadecaquasitruncated tesseractihexadecachora
Cells	160+160 truncated tetrahedra, 40 truncated cubes, 40 quasitruncated hexahedra, 80 cuboctatruncated cuboctahedra
Faces	320+320 triangles, 640 hexagons, 240 octagons, 240 octagrams
Edges	480+960+960
Vertices	960
Vertex figure	Skewed tetragonal disphenoidal pyramid, edge lengths 1 (bases of disphenoid), √3 (lacings of disphenoid), √2+√2 (lacings to base 1), and √2–√2 (lacings to base 2)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{13}}{2} ≈ 1.80278$
Hypervolume	86
Diteral angles	Thaquitoth–tut–deca: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505^\circ$
	Thaquitoth–quith–thaquitoth: 90°
	Thatoth–tic–thatoth: 90°
	Thaquitoth–cotco–thatoth: 90°
	Thatoth–tut–deca: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495^\circ$
Related polytopes
Army	Semi-uniform Prin, edge lengths $\sqrt2-1$ (small rhombicuboctahedra), 1 (remaining edges)
Regiment	Danbitot
Conjugate	Dispenteractibitruncated triacontaditeron
Abstract & topological properties
Flag count	115200
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	No
Nature	Tame

The dispenteractibitruncated triacontaditeron, or danbitot, is a nonconvex uniform polyteron. It consists of 10 tesseractihexadecatruncated tesseractihexadecachora, 10 tesseractihexadecaquasitruncated tesseractihexadecachora, and 32 decachora. 1 decachoon, 2 tesseractihexadecatruncated tesseractihexadecachora, and 2 tesseractihexadecaquasitruncated tesseractihexadecachora join at each vertex.

Vertex coordinates

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

• $\left(±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 10: Greater Truncates" (#731).

• Klitzing, Richard. "danbitot".