Great snub icosidodecahedron
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Great snub icosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Gosid |
Coxeter diagram | s5/2s3s () |
Elements | |
Faces | 20+60 triangles, 12 pentagrams |
Edges | 30+60+60 |
Vertices | 60 |
Vertex figure | Irregular pentagon, edge lengths 1, 1, 1, 1, (√5–1)/2 |
Measures (edge length 1) | |
Circumradius | ≈ 0.81608 |
Volume | ≈ 7.67391 |
Dihedral angles | 5/2–3: ≈ 138.82237° |
3–3: ≈ 126.82315° | |
Central density | 7 |
Number of external pieces | 300 |
Level of complexity | 26 |
Related polytopes | |
Army | Non-uniform snub dodecahedron |
Regiment | Gosid |
Dual | Great pentagonal hexecontahedron |
Conjugates | Snub dodecahedron, Great inverted snub icosidodecahedron, great inverted retrosnub icosidodecahedron |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | H_{3}+, order 60 |
Convex | No |
Nature | Tame |
The great snub icosidodecahedron or gosid is a uniform polyhedron. It consists of 60 snub triangles, 20 additional triangles, and 12 pentagrams. Four triangles and one pentagram meeting at each vertex.
Measures
The circumradius R ≈ 0.81608 of the great snub icosidodecahedron with unit edge length is the second to largest real root of:
Its volume V ≈ 7.67391 is given by the second to largest real root of:
These same polynomials define the circumradii and volumes of the snub dodecahedron, the great inverted snub icosidodecahedron, and the great inverted retrosnub icosidodecahedron.
Related polyhedra
The great disnub icosidodecahedron is a uniform polyhedron compound composed of the 2 opposite chiral forms of the great snub icosidodecahedron.
Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|
Great icosahedron | gike | {3,5/2} | x3o5/2o () | |
Truncated great icosahedron | tiggy | t{3,5/2} | x3x5/2o () | |
Great icosidodecahedron | gid | r{3,5/2} | o3x5/2o () | |
Truncated great stellated dodecahedron (degenerate, ike+2gad) | t{5/2,3} | o3x5/2x () | ||
Great stellated dodecahedron | gissid | {5/2,3} | o3o5/2x () | |
Small complex rhombicosidodecahedron (degenerate, sidtid+rhom) | sicdatrid | rr{3,5/2} | x3o5/2x () | |
Truncated great icosidodecahedron (degenerate, ri+12(10/2)) | tr{3,5/2} | x3x5/2x () | ||
Great snub icosidodecahedron | gosid | sr{3,5/2} | s3s5/2s () |
External links
- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#67).
- Klitzing, Richard. "gosid".
- Wikipedia Contributors. "Great snub icosidodecahedron".
- McCooey, David. "Great Snub Icosidodecahedron"