Great discellidispenteractitriacontaditeron

Great discellidispenteractitriacontaditeron
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Gidacadint
Coxeter diagram	x3x3o3x *b4/3x4*c ()
Elements
Tera	40 small rhombicuboctahedral prisms, 40 quasitruncated cuboctahedral prisms, 32 prismatorhombated pentachora, 10 great cubihexadecadisoctachora, 10 small skewverted prismatohexadecadisoctachora
Cells	320 triangular prisms, 240+480 cubes, 320 hexagonal prisms, 160 truncated tetrahedra, 160 cuboctahedra, 240 octagrammic prisms, 80 small rhombicuboctahedra, 80 great cubicuboctahedra, 80 quasitruncated cuboctahedra
Faces	640+640 triangles, 480+960+960+960+960 squares, 640 hexagons, 480 octagrams
Edges	960+1920+1920+1920
Vertices	1920
Vertex figure	Skewed wedge pyramid, base wedge edge lengths 1 (2), √2 (5), and √2–√2 (2), side edge lengths √2 (4) and √3 (2)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {17-4{\sqrt {2}}}}{2}}\approx 1.68398$
Hypervolume	${\frac {3050+973{\sqrt {2}}}{30}}\approx 147.53433$
Diteral angles	Gichado–quitco–quitcope: 135°
	Skiviphado–sirco–sircope: 135°
	Prip–hip–quitcope: $\arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }$
	Gichado–tut–prip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Skiviphado–gocco–gichado: 90°
	Skiviphado–stop–quitcope: 90°
	Gichado–cube–sircope: 90°
	Sircope–cube–quitcope: 90°
	Skiviphado–co–prip: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
	Prip–trip–sircope: $\arccos \left({\frac {\sqrt {10}}{5}}\right)\approx 50.76848^{\circ }$
Related polytopes
Army	Semi-uniform Captint, edge lengths ${\sqrt {2}}-1$ (truncated cubic prisms), $2-{\sqrt {2}}$ (remaining edges)
Regiment	Gidacadint
Conjugate	Small discellidispenteractitriacontaditeron
Abstract & topological properties
Flag count	345600
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	No
Nature	Tame

The great discellidispenteractitriacontaditeron, or gidacadint, is a nonconvex uniform polyteron. It consists of 10 small skewverted prismatohexadecadisoctachora, 10 great cubihexadecadisoctachora, 32 prismatorhombated pentachora, 40 small rhombicuboctahedral prisms, and 40 quasitruncated cuboctahedral prisms. 1 small skewverted prismatohexadecadisoctachoron, 1 great cubihexadecadisoctachoron, 1 prismatorhombated pentachoron, 1 small rhombicuboctahedral prism, and 2 quasitruncated cuboctahedral prisms meet at each vertex.

The great discellidispenteractitriacontaditeron contains the vertices and edges of a tesseractihexadecaquasitruncated prismatotesseractihexadecachoric prism and octagonal-quasitruncated cuboctahedral duoprism.

Vertex coordinates

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

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

Related polytopes

The great discellidispenteractitriacontaditeron is the colonel of a regiment that contains 15 members.