Tridiminished rhombicosidodecahedron |
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Rank | 3 |
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Type | CRF |
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Notation |
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Bowers style acronym | Tedrid |
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Elements |
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Faces | 1+1+3 triangles, 3+3+3+6 squares, 3+3+3 pentagons, 3 decagons |
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Edges | 3+3+3+3+3+3+3+6+6+6+6+6+6+6+6+6 |
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Vertices | 3+3+3+6+6+6+6+6+6 |
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Vertex figures | 15 isosceles trapezoids, edge length 1, √2, (1+√5)/2, √2 |
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| 30 scalene triangles, edge lengths √2, (1+√5)/2, √(5+√5)/2 |
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Measures (edge length 1) |
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Circumradius | |
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Volume | |
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Dihedral angles | 3–4: |
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| 4–5: |
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| 4–10: |
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| 5–10: |
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Central density | 1 |
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Number of external pieces | 32 |
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Level of complexity | 50 |
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Related polytopes |
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Army | Tedrid |
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Regiment | Tedrid |
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Dual | Tristellated deltoidal hexecontahedron |
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Conjugate | Trireplenished quasirhombicosidodecahedron |
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Abstract & topological properties |
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Flag count | 300 |
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Euler characteristic | 2 |
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Surface | Sphere |
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Orientable | Yes |
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Genus | 0 |
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Properties |
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Symmetry | A2×I, order 6 |
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Convex | Yes |
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Nature | Tame |
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The tridiminished rhombicosidodecahedron is one of the 92 Johnson solids (J83). It consists of 1+1+3 triangles, 3+3+3+6 squares, 3+3+3 pentagons, and 3 decagons. It can be constructed by removing three pentagonal cupolaic caps of the small rhombicosidodecahedron.
A tridiminished rhombicosidodecahedron of edge length 1 has vertices given by:
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- .