Trigyrate 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 | Tagyrid |
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Elements |
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Faces | 1+1+3+3+6+6 triangles, 3+3+3+3+6+6+6 squares, 3+3+3+3 pentagons |
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Edges | 8×3+16×6 |
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Vertices | 3+3+3+3+6+6+6+6+6+6+6+6 |
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Vertex figures | 15+15 isosceles trapezoids, edge length 1, √2, (1+√5)/2, √2 |
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| 30 irregular tetragons, edge lengths 1, √2, √2, (1+√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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| 3–5: |
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| 4–4: |
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| 4–5: |
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Central density | 1 |
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Number of external pieces | 62 |
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Level of complexity | 80 |
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Related polytopes |
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Army | Tagyrid |
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Regiment | Tagyrid |
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Dual | Trideltogyrate deltoidal hexecontahedron |
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Conjugate | Trigyrate quasirhombicosidodecahedron |
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Abstract & topological properties |
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Flag count | 480 |
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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 trigyrate rhombicosidodecahedron is one of the 92 Johnson solids (J75). It consists of 1+1+3+3+6+6 triangles, 3+3+3+3+6+6+6 squares, and 3+3+3+3 pentagons. It can be constructed by rotating three mutually non-adjacent pentagonal cupolaic caps of the small rhombicosidodecahedron by 36°.
A trigyrate rhombicosidodecahedron of edge length 1 has vertices given by: