Great inverted retrosnub icosidodecahedron
| Great inverted retrosnub icosidodecahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Girsid |
| Coxeter diagram | s5/3s3/2s (     ) |
| Elements | |
| Faces | 20+60 triangles, 12 pentagrams |
| Edges | 30+60+60 |
| Vertices | 60 |
| Vertex figure | Irregular pentagram, edge lengths 1, 1, 1, 1, (√5–1)/2  |
| Measures (edge length 1) | |
| Circumradius | ≈ 0.58000 |
| Volume | ≈ 1.03760 |
| Dihedral angles | 5/2–3: ≈ 67.31029° |
| 3–3: ≈ 21.72466° | |
| Central density | 37 |
| Number of external pieces | 1800 |
| Level of complexity | 139 |
| Related polytopes | |
| Army | Non-uniform Snid |
| Regiment | Girsid |
| Dual | Great pentagrammic hexecontahedron |
| Conjugates | Snub dodecahedron, great snub icosidodecahedron, great inverted snub icosidodecahedron |
| Abstract & topological properties | |
| Flag count | 600 |
| Euler characteristic | 2 |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | H3+, order 60 |
| Convex | No |
| Nature | Tame |
The great inverted retrosnub icosidodecahedron or girsid, also called the great retrosnub icosidodecahedron, is a uniform polyhedron. It consists of 60 snub triangles, 20 additional triangles, and 12 pentagrams. Four triangles and one pentagram meet at each vertex.
Measures[edit | edit source]
The circumradius R ≈ 0.58000 of the great inverted retrosnub icosidodecahedron with unit edge length is the smallest positive real root of:
Its volume V ≈ 1.03760 is given by the smallest positive real root of:
These same polynomials define the circumradii and volumes of the snub dodecahedron, the great snub icosidodecahedron, and the great inverted snub icosidodecahedron.
Related polyhedra[edit | edit source]
The great diretrosnub icosidodecahedron is a uniform polyhedron compound composed of the 2 opposite chiral forms of the great inverted retrosnub icosidodecahedron.
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#73).
- Klitzing, Richard. "girsid".
- Wikipedia Contributors. "Great retrosnub icosidodecahedron".
- McCooey, David. "Great Retrosnub Icosidodecahedron"