Snub icosidodecadodecahedron
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Snub icosidodecadodecahedron | |
---|---|
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 | H_{3}+, order 60 |
Convex | No |
Nature | Tame |
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.
Measures[edit | edit source]
The circumradius R ≈ 1.12690 of the snub icosidodecadodecahedron with unit edge length is the greatest real root of
Its volume V ≈ 14.64198 is given by the positive real root of
Related polyhedra[edit | edit source]
The disnub icosidodecadodecahedron is a uniform polyhedron compound composed of the 2 chiral forms of the snub icosidodecadodecahedron.
Name | OBSA | CD diagram | Picture |
---|---|---|---|
Ditrigonary dodecadodecahedron | ditdid | ||
Small complex icosidodecahedron (degenerate, ike+gad) | cid | ||
Great complex icosidodecahedron (degenerate, sissid+gike) | gacid | ||
Icosidodecadodecahedron | ided | ||
Small ditrigonal dodecicosidodecahedron | sidditdid | ||
Great ditrigonal dodecicosidodecahedron | gidditdid | ||
Icosidodecatruncated icosidodecahedron | idtid | ||
Snub icosidodecadodecahedron | sided |
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#71).
- Klitzing, Richard. "sided".
- Wikipedia Contributors. "Snub icosidodecadodecahedron".
- McCooey, David. "Snub Icosidodecadodecahedron"