Small hexacosihecatonicosidishecatonicosachoron

Small hexacosihecatonicosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sixhidy
Coxeter diagram	o3o3x5x5/3*a ()
Elements
Cells	600 tetrahedra, 120 great stellated dodecahedra, 120 truncated dodecahedra, 120 truncated great dodecahedra
Faces	2400 triangles, 1440 pentagrams, 1440 decagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular retroantipodium, edge lengths 1 (large base), (√5–1)/2 (small base), and √(5+√5)/2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {11+3{\sqrt {5}}}{2}}}\approx 2.97558$
Hypervolume	$5{\frac {905+544{\sqrt {5}}}{4}}\approx 2651.77622$
Dichoral angles	Gissid–5/2–tigid: 72°
	Tid–10–tigid: 36°
	Tet–3–tid: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
Number of external pieces	69120
Level of complexity	191
Related polytopes
Army	Semi-uniform Sidpixhi, edge lengths ${\frac {3-{\sqrt {5}}}{2}}$ (dodecahedra), 1 (tetrahedra)
Regiment	Shihix
Conjugate	Great hexacosihecatonicosidishecatonicosachoron
Abstract & topological properties
Flag count	115200
Euler characteristic	–480
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

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

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small hecatonicosihecatonicosihexacosichoron.

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#506).

• Klitzing, Richard. "sixhidy".