Snub icosidodecadodecahedron

The snub icosidodecadodecahedron or sided, is a uniform polyhedron. It consists of 60 snub triangles, 20 additional triangles, 12 pentagrams, and 12 pentagons. Four triangles, one pentagon, and one pentagram meeting at each vertex. It can be constructed by alternation of the icosidodecatruncated icosidodecahedron and then setting all edge lengths to be equal.

Snub icosidodecadodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sided
Coxeter diagram	s5/3s3s5*a ()
Elements
Faces	20+60 triangles, 12 pentagons, 12 pentagrams
Edges	60+60+60
Vertices	60
Vertex figure	Irregular hexagon, edge lengths 1, 1, 1, (√5–1)/2, 1, (1+√5)/2
Measures (edge length 1)
Circumradius	≈ 1.12690
Volume	≈ 14.64198
Dihedral angles	3–3: ≈ 146.78125°
	5–3: ≈ 120.43401°
	5/2–3: ≈ 7.35214°
Central density	4
Number of external pieces	452
Level of complexity	31
Related polytopes
Army	Non-uniform Snid
Regiment	Sided
Dual	Medial hexagonal hexecontahedron
Conjugate	Snub icosidodecadodecahedron
Convex core	Dodecahedron
Abstract & topological properties
Flag count	720
Euler characteristic	-16
Orientable	Yes
Genus	9
Properties
Symmetry	H3+, order 60
Convex	No
Nature	Tame

Measures

The circumradius R ≈ 1.12690 of the snub icosidodecadodecahedron with unit edge length is the greatest real root of

$64x^6-128x^4+68x^2-11.$

Its volume V ≈ 14.64198 is given by the positive real root of

$729x^6-155520x^4-10125x^2-33153125.$

Related polyhedra

The disnub icosidodecadodecahedron is a uniform polyhedron compound composed of the 2 chiral forms of the snub icosidodecadodecahedron.

External links

• Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#71).

• Klitzing, Richard. "sided".

• Wikipedia Contributors. "Snub icosidodecadodecahedron".
• McCooey, David. "Snub Icosidodecadodecahedron"