Small icosicosidodecahedron
Small icosicosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Siid |
Coxeter diagram | x5/2o3x3*a () |
Elements | |
Faces | 20 triangles, 12 pentagrams, 20 hexagons |
Edges | 60+60 |
Vertices | 60 |
Vertex figure | Isosceles trapezoid, edge lengths 1, √3, (√5–1)/2, √3 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 5/2–6: |
3–6: | |
Central density | 2 |
Number of external pieces | 92 |
Level of complexity | 7 |
Related polytopes | |
Army | Semi-uniform Srid, edge lengths (pentagons), 1 (triangles) |
Regiment | Siid |
Dual | Small icosacronic hexecontahedron |
Conjugate | Great icosicosidodecahedron |
Convex core | Truncated icosahedron |
Abstract & topological properties | |
Flag count | 480 |
Euler characteristic | –8 |
Orientable | Yes |
Properties | |
Symmetry | H_{3}, order 120 |
Flag orbits | 4 |
Convex | No |
Nature | Tame |
The small icosicosidodecahedron, or siid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 20 hexagons. One triangle, one pentagram, and two hexagons join at each vertex.
A semi-uniform variant of this polyhedron can be constructed as a rectified small ditrigonary icosidodecahedron.
Vertex coordinates[edit | edit source]
A small icosicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:
Representations[edit | edit source]
A small icosicosidodecahedron has the following Coxeter diagrams:
- x3x5/2o3*a ()
- ß5o3x () (as holosnub)
Related polyhedra[edit | edit source]
The small icosicosidodecahedron is the colonel of a three-member regiment that also includes the small ditrigonal dodecicosidodecahedron and the small dodecicosahedron.
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 4: Trapeziverts" (#51).
- Klitzing, Richard. "siid".
- Wikipedia contributors. "Small icosicosidodecahedron".
- McCooey, David. "Small Icosicosidodecahedron"