Snub hexacosihecatonicosachoron

Snub hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Snixhi
Coxeter diagram	s5s3s3s ()
Elements
Cells	7200 irregular tetrahedra, 1200 triangular gyroprisms, 720 pentagonal gyroprisms, 600 snub tetrahedra, 120 snub dodecahedra
Faces	7200+7200+7200+7200 scalene triangles, 2400+2400 triangles, 1440 pentagons
Edges	3600+3600+3600+7200+7200+7200
Vertices	7200
Vertex figure	Polyhedron with 2 pentagons, 2 tetragons, and 4 triangles
Measures (as derived from unit-edge great disprismatohexacosihecatonicosachoron)
Edge lengths	Edges from diagonals of original squares (3600+3600+3600): ${\sqrt {2}}\approx 1.41421$
	Edges of equilateral triangles (7200+7200): ${\sqrt {3}}\approx 1.73205$
	Edges of pentagons (7200): ${\sqrt {\frac {5+{\sqrt {5}}}{2}}}\approx 1.90211$
Circumradius	${\sqrt {83+36{\sqrt {5}}}}\approx 12.78665$
Central density	1
Related polytopes
Army	Snixhi
Regiment	Snixhi
Dual	Enneahedral heptachilliadiacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4+, order 7200
Convex	Yes
Nature	Tame

The snub hexacosihecatonicosachoron, omnisnub hecatonicosachoron, omnisnub hexacosichoron, or snixhi is a convex isogonal polychoron that consists of 120 snub dodecahedra, 600 snub tetrahedra, 720 pentagonal gyroprisms, 1200 triangular gyroprisms, and 7200 irregular tetrahedra. Each vertex joins 4 tetrahedra and 1 of each of the other 4 cell types. It can be obtained through the process of alternating the great disprismatohexacosihecatonicosachoron. However, it cannot be made uniform, as it generally as 6 edge lengths, which can be minimized to no fewer than 3 different sizes.

The lowest possible ratio between the longest and shortest edges is approximately $1.2661327136794291861309032$.

External links

• Klitzing, Richard. "snahi".
• Wikipedia contributors. "Full snub 120-cell".