Small snub icosicosidodecahedron
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Small snub icosicosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Seside |
Coxeter diagram | s5/2s3s3*a () |
Elements | |
Faces | 60 triangles, 40 triangles as 20 hexagrams, 12 pentagrams |
Edges | 60+60+60 |
Vertices | 60 |
Vertex figure | Mirror-symmetric hexagon, edge lengths 1, 1, 1, 1, 1, (√5–1)/2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 5/2–3: |
3–3: | |
Central density | 2 |
Number of external pieces | 212 |
Level of complexity | 15 |
Related polytopes | |
Army | Semi-uniform ti, edge lengths (pentagons), (between ditrigons) |
Regiment | Seside |
Dual | Small hexagonal hexecontahedron |
Conjugate | Small retrosnub icosicosidodecahedron |
Convex core | Truncated pentakis dodecahedron |
Abstract & topological properties | |
Flag count | 720 |
Euler characteristic | -8 |
Orientable | Yes |
Genus | 5 |
Properties | |
Symmetry | H_{3}, order 120 |
Convex | No |
Nature | Tame |
The small snub icosicosidodecahedron, or seside, is a uniform polyhedron. It consists of 60 snub triangles, 40 more triangles that create 20 hexagrams due to pairs falling in the same plane, and 12 pentagrams. Five triangles and one pentagram meet at each vertex.
It can be obtained as a holosnub truncated icosahedron, after adjusting all edge lengths to be equal.
Vertex coordinates[edit | edit source]
A small snub icosicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:
Representations[edit | edit source]
A small snub icosicosidodecahedron has the following Coxeter diagrams:
- s5/2s3s3*a
- o5ß3ß (as holosnub)
Related polyhedra[edit | edit source]
Name | OBSA | CD diagram | Picture |
---|---|---|---|
Small ditrigonary icosidodecahedron | sidtid | x5/2o3o3*a () | |
(degenerate, double cover of id) | x5/2x3o3*a () | ||
(degenerate, double cover of ike) | o5/2o3x3*a () | ||
Small icosicosidodecahedron | siid | x5/2o3x3*a () | |
(degenerate, double cover of ti) | x5/2x3x3*a () | ||
Small snub icosicosidodecahedron | seside | s5/2s3s3*a () |
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#68).
- Klitzing, Richard. "seside".
- Wikipedia contributors. "Small snub icosicosidodecahedron".
- McCooey, David. "Small Snub Icosicosidodecahedron"