Snub dodecadodecahedron
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Snub dodecadodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Siddid |
Coxeter diagram | s5/2s5s () |
Elements | |
Faces | 60 triangles, 12 pentagons, 12 pentagrams |
Edges | 30+60+60 |
Vertices | 60 |
Vertex figure | Irregular pentagon, edge lengths 1, 1, (√5–1)/2, 1, (1+√5)/2 |
Measures (edge length 1) | |
Circumradius | ≈ 1.27444 |
Volume | ≈ 18.25642 |
Dihedral angles | 5/2–3: ≈ 157.77792° |
3–3: ≈ 151.48799° | |
5–3: ≈ 129.79515° | |
Central density | 3 |
Number of pieces | 432 |
Level of complexity | 29 |
Related polytopes | |
Army | Non-uniform snub dodecahedron |
Regiment | Siddid |
Dual | Medial pentagonal hexecontahedron |
Conjugate | Inverted snub dodecadodecahedron |
Abstract properties | |
Euler characteristic | -6 |
Topological properties | |
Orientable | Yes |
Genus | 4 |
Properties | |
Symmetry | H_{3}+, order 60 |
Convex | No |
Nature | Tame |
The snub dodecadodecahedron or siddid, is a uniform polyhedron. It consists of 60 snub triangles, 12 pentagrams, and 12 pentagons. Three triangles, 1 pentagon, and one pentagram meeting at each vertex.
Measures[edit | edit source]
The circumradius R ≈ 1.27444 of the snub dodecadodecahedron with unit edge length is the largest real root of:
Its volume V ≈ 18.25642 is given by the largest real root of:
These same polynomials define the circumradius and volume of the inverted snub dodecadodecahedron.
Related polyhedra[edit | edit source]
The disnub dodecadodecahedron is a uniform polyhedron compound composed of the 2 opposite chiral forms of the snub dodecadodecahedron.
Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|
Great dodecahedron | gad | {5,5/2} | x5o5/2o () | |
Truncated great dodecahedron | tigid | t{5,5/2} | x5x5/2o () | |
Dodecadodecahedron | did | r{5,5/2} | o5x5/2o () | |
Truncated small stellated dodecahedron (degenerate, triple cover of doe) | t{5/2,5} | o5x5/2x () | ||
Small stellated dodecahedron | sissid | {5/2,5} | o5o5/2x () | |
Rhombidodecadodecahedron | raded | rr{5,5/2} | x5o5/2x () | |
Truncated dodecadodecahedron (degenerate, sird+12(10/2)) | tr{5,5/2} | x5x5/2x () | ||
Snub dodecadodecahedron | siddid | sr{5,5/2} | s5s5/2s () |
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#66).
- Klitzing, Richard. "siddid".
- Wikipedia Contributors. "Snub dodecadodecahedron".
- McCooey, David. "Snub Dodecadodecahedron"