Small dishexacosidishecatonicosachoron

Small dishexacosidishecatonicosachoron
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sadixady
Coxeter diagram	x3x3o3o5/2*a ()
Elements
Cells	600 tetrahedra, 120 great stellated dodecahedra, 600 truncated tetrahedra, 120 truncated great icosahedra
Faces	2400 triangles, 1440 pentagrams, 2400 hexagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular antipodium, edge lengths 1 (large base), (√5–1)/2 (small base), and √3 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Tet–3–tut:
	Tiggy–6–tut:
	Gissid–5/2–tiggy: 144°
Number of external pieces	57120
Level of complexity	293
Related polytopes
Army	Semi-uniform Sidpixhi, edge lengths (dodecahedra), (tetrahedra)
Regiment	Sadixady
Conjugate	Great dishexacosidishecatonicosachoron
Abstract & topological properties
Flag count	115200
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

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

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a small dishexacosidishecatonicosachoron of edge length 1 are given by all permutations of:

$\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {5-{\sqrt {5}}}{2}},\,\pm {\frac {5-{\sqrt {5}}}{2}},\,\pm {\frac {5-{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {9-{\sqrt {5}}}{4}}\right),$
$\left(\pm 1,\,\pm 1,\,\pm 1,\,\pm {\frac {3-{\sqrt {5}}}{2}}\right),$

along with all even permutations of:

$\left(0,\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {7-{\sqrt {5}}}{4}},\,\pm {\frac {2-{\sqrt {5}}}{2}}\right),$
$\left(0,\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {\sqrt {5}}{2}}\right),$
$\left(0,\,\pm {\frac {1}{2}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3{\sqrt {5}}-1}{4}}\right),$
$\left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {9-{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}}\right),$
$\left(0,\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}}\right),$
$\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm 1\right),$
$\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {5-{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {7-{\sqrt {5}}}{4}},\,\pm {\frac {5-{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {3{\sqrt {5}}-1}{4}},\,\pm {\frac {5-{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {5-{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm 1,\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {3{\sqrt {5}}-1}{4}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {7-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}}\right),$
$\left(\pm 1,\,\pm {\frac {\sqrt {5}}{2}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}}\right).$