Great snub dodecicosidodecahedron
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Great snub dodecicosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Gisdid |
Coxeter diagram | s5/3s5/2s3*a () |
Elements | |
Faces | 20+60 triangles, 24 pentagrams |
Edges | 60+60+60 |
Vertices | 60 |
Vertex figure | Irregular hexagon, edge lengths 1, 1, 1, (√5–1)/2, 1, (√5–1)/2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 5/2–3 #1: |
3–3: | |
5/2–3 #2: | |
Central density | 10 |
Number of external pieces | 660 |
Level of complexity | 42 |
Related polytopes | |
Army | Semi-uniform srid, edge lengths (pentagons), (triangles) |
Regiment | Gisdid |
Dual | Great hexagonal hexecontahedron |
Conjugate | Great snub dodecicosidodecahedron |
Abstract & topological properties | |
Flag count | 720 |
Euler characteristic | -16 |
Orientable | Yes |
Genus | 9 |
Properties | |
Symmetry | H_{3}+, order 60 |
Chiral | Yes |
Convex | No |
Nature | Tame |
The great snub dodecicosidodecahedron, or gisdid, is a uniform polyhedron. It consists of 60 snub triangles, 20 more triangles, and 24 pentagrams that fall in coplanar pairs of one prograde, one retrograde. Four triangles and two pentagrams meet at each vertex.
It is the only chiral uniform polyhedron with an achiral convex hull. As such, it cannot be made into a compound with its reflection. If the pentagrams are removed, however, the disnub icosahedron is formed.
This polyhedron's edges are a subset of those of the great dirhombicosidodecahedron, and it shares the same vertices.
Vertex coordinates[edit | edit source]
A great snub dodecicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:
Related polyhedra[edit | edit source]
Name | OBSA | CD diagram | Picture |
---|---|---|---|
Great complex icosidodecahedron (degenerate, sissid+gike) | gacid | x5/3o5/2o3*a () | |
Great dodecicosidodecahedron | gaddid | x5/3x5/2o3*a () | |
(degenerate, double cover of gissid) | o5/3x5/2o3*a () | ||
(degenerate, ditdid+gidtid) | o5/3x5/2x3*a () | ||
Great complex icosidodecahedron (degenerate, sissid+gike) | gacid | o5/3o5/2x3*a () | |
(degenerate, double cover of sidhei) | x5/3o5/2x3*a () | ||
(degenerate, giddy+12(10/2)) | x5/3x5/2x3*a () | ||
Great snub dodecicosidodecahedron | gisdid | s5/3s5/2s2*a () |
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#72).
- Klitzing, Richard. "gisdid".
- Wikipedia contributors. "Great snub dodecicosidodecahedron".
- McCooey, David. "Great Snub Dodecicosidodecahedron"