Great dishexacosidishecatonicosachoron

Great dishexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gadixady
Coxeter diagram	x3x3/2o3o5*a ()
Elements
Cells	600 tetrahedra, 120 dodecahedra, 600 truncated tetrahedra, 120 truncated icosahedra
Faces	2400 triangles, 1440 pentagons, 2400 hexagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular retroantipodium, edge lengths 1 (small base), (1+√5)/2 (large base), and √3 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {13+3{\sqrt {5}}}{2}}}\approx 3.13912$
Hypervolume	$5{\frac {365+322{\sqrt {5}}}{2}}\approx 2712.53471$
Dichoral angles	Doe–5–ti: 72°
	Tet–3–tut: $\arccos \left({\frac {3{\sqrt {5}}-1}{8}}\right)\approx 44.47751^{\circ }$
	Ti–6–tut: $\arccos \left({\frac {\sqrt {10}}{4}}\right)\approx 37.37737^{\circ }$
Number of external pieces	909840
Level of complexity	1984
Related polytopes
Army	Thi, edge length ${\frac {3-{\sqrt {5}}}{2}}$
Regiment	Gidthixhi
Conjugate	Small dishexacosidishecatonicosachoron
Abstract & topological properties
Flag count	115200
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great dishexacosidishecatonicosachoron, or gadixady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, 600 truncated tetrahedra, and 120 truncated icosahedra. 1 tetrahedron, 1 dodecahedron, 3 truncated tetrahedra, and 3 truncated icosahedra join at each vertex.

Gallery

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great ditrigonal hecatonicosihexacosihecatonicosachoron.

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#492).

• Klitzing, Richard. "gadixady".