Great icosidodecahedron
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Great icosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Gid |
Coxeter diagram | o5/2x3o () |
Elements | |
Faces | 20 triangles, 12 pentagrams |
Edges | 60 |
Vertices | 30 |
Vertex figure | Rectangle, edge lengths 1 and (√5–1)/2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angle | |
Central density | 7 |
Number of external pieces | 132 |
Level of complexity | 10 |
Related polytopes | |
Army | Id |
Regiment | Gid |
Dual | Great rhombic triacontahedron |
Conjugate | Icosidodecahedron |
Convex core | Icosahedron |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | H_{3}, order 120 |
Convex | No |
Nature | Tame |
The great icosidodecahedron or gid is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagrams, with two of each joining at a vertex. It can be derived as a rectified great stellated dodecahedron or great icosahedron.
Vertex coordinates
A great icosidodecahedron of side length 1 has vertex coordinates given by all permutations of
and even permutations of
The first set of vertices corresponds to a scaled octahedron which can be inscribed into the icosidodecahedron.
Related polyhedra
The great icosidodecahedron is the colonel of a three-member regiment that also includes the great icosihemidodecahedron and great dodecahemidodecahedron.
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 3: Quasiregulars" (#30).
- Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#1 under gid).
- Klitzing, Richard. "gid".
- Wikipedia Contributors. "Great icosidodecahedron".
- McCooey, David. "Great Icosidodecahedron"