Great snub icosidodecahedron
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.
| 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 Snid |
| Regiment | Gosid |
| Dual | Great pentagonal hexecontahedron |
| Conjugates | Snub dodecahedron, Great inverted snub icosidodecahedron, great inverted retrosnub icosidodecahedron |
| Abstract & topological properties | |
| Flag count | 600 |
| Euler characteristic | 2 |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | H3+, order 60 |
| Convex | No |
| Nature | Tame |
MeasuresEdit
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 polyhedraEdit
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 linksEdit
- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#67).
- Klitzing, Richard. "gosid".
- Wikipedia Contributors. "Great snub icosidodecahedron".
- McCooey, David. "Great Snub Icosidodecahedron"