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In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (icosi-) triangular faces and twelve (dodeca-) pentagonal faces. An icosidodecahedron has 30 identical vertices , with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon.
3D model of a great icosidodecahedron. In geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U 54. It has 32 faces (20 triangles and 12 pentagrams), 60 edges, and 30 vertices. [1] It is given a Schläfli symbol r{3, 5 ⁄ 2}. It is the rectification of the great stellated dodecahedron and the great icosahedron.
The truncated icosidodecahedron is the convex hull of a rhombicosidodecahedron with cuboids above its 30 squares, whose height to base ratio is φ. The rest of its space can be dissected into nonuniform cupolas, namely 12 between inner pentagons and outer decagons and 20 between inner triangles and outer hexagons .
In geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagrams and 20 triangles . All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping edges as topological polyhedron.
The pentakis icosidodecahedron is a common geometry for geodesic domes derived from the icosahedron. Buckminster Fuller referred to it as the 2-frequency alternate geodesic subdivision of the icosahedron, because the edges are divided into 2 equal parts and then lengthed slightly to keep the new vertices on a geodesic great circle, creating a polyhedron with two distinct edge lengths and face ...
3D model of a great retrosnub icosidodecahedron. In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U 74. It has 92 faces (80 triangles and 12 pentagrams), 150 edges, and 60 vertices. [1] It is given a Schläfli symbol sr{3 ⁄ 2, 5 ⁄ 3}.
3D model of a great snub icosidodecahedron. In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U 57. It has 92 faces (80 triangles and 12 pentagrams), 150 edges, and 60 vertices. [1] It can be represented by a Schläfli symbol sr{5 ⁄ 2,3}, and Coxeter-Dynkin diagram.
3D model of a great truncated icosidodecahedron. In geometry, the great truncated icosidodecahedron (or great quasitruncated icosidodecahedron or stellatruncated icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U 68. It has 62 faces (30 squares, 20 hexagons, and 12 decagrams), 180 edges, and 120 vertices. [1]