Great dispenteractirhombated triacontaditeron

Great dispenteractirhombated triacontaditeron
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Gadinnert
Coxeter diagram	o3x3x3x *b4/3x4*c ()
Elements
Tera	40 quasitruncated hexahedral prisms, 32 great rhombated pentachora, 10 tesseractihexadecaquasitruncated tesseractihexadecachora, 10 tesseractihexadecatruncated prismatotesseractihexadecachora
Cells	320 triangular prisms, 160 truncated tetrahedra, 240 octagrammic prisms, 160 truncated octahedra, 80 quasitruncated hexahedra, 40 great rhombicuboctahedra, 80 cuboctatruncated cuboctahedra
Faces	640 triangles, 480+960 squares, 320+640 hexagons, 240 octagons, 480 octagrams
Edges	960+960+960+1920
Vertices	1920
Vertex figure	Sphenoidal pyramid, edge lengths 1 (1), √2 (3), √3 (3), √2+√2 (1), and √2–√2 (2)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {19+2{\sqrt {2}}}}{2}}\approx 2.33605$
Hypervolume	${\frac {10680-1249{\sqrt {2}}}{30}}\approx 414.87842297.12158$
Diteral angles	Thaquitoth–quith–quithip: 135°
	Grip–trip–quithip: $\arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }$
	Thaquitoth–tut–grip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Thatpath–girco–thatpath: 90°
	Thatpath–cotco–thaquitoth: 90°
	Thatpath–stop–quithip: 90°
	Thatpath–toe–grip: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Related polytopes
Army	Semi-uniform Cogart, edge lengths ${\sqrt {2}}-1$ (small rhombicuboctahedra), 1 (hexagons of duoprisms)
Regiment	Gadinnert
Conjugate	Small dispenteractirhombated triacontaditeron
Abstract & topological properties
Flag count	230400
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	No
Nature	Tame

The great dispenteractirhombated triacontaditeron, or gadinnert, is a nonconvex uniform polyteron. It consists of 10 tesseractihexadecatruncated prismatotesseractihexadecachora, 32 great rhombated pentachora, 10 tesseractihexadecaquasitruncated tesseractihexadecachora, and 40 quasitruncated hexahedral prisms. One great rhombated pentachoron, 1 tesseractihexadecaquasitruncated tesseractihexadecachoron, 1 quasitruncated hexahedral prism, and 2 tesseractihexadecatruncated prismatotesseractihexadecachora join at each vertex.

Vertex coordinates

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

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

External links

• Bowers, Jonathan. "Category 10: Greater Truncates" (#739).

• Klitzing, Richard. "gadinnert".