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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.
In geometry, the small ditrigonal icosidodecahedron (or small ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U 30. It has 32 faces (20 triangles and 12 pentagrams ), 60 edges, and 20 vertices. [ 1 ]
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 icositruncated dodecadodecahedron or icosidodecatruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U 45. Convex hull
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 ]
In geometry, the small icosicosidodecahedron (or small icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U 31. It has 52 faces (20 triangles , 12 pentagrams , and 20 hexagons ), 120 edges, and 60 vertices.
In geometry, the great inverted snub icosidodecahedron (or great vertisnub icosidodecahedron) is a uniform star polyhedron, indexed as U 69. It is given a Schläfli symbol sr{5 ⁄ 3,3}, and Coxeter-Dynkin diagram. In the book Polyhedron Models by Magnus Wenninger, the polyhedron is misnamed great snub icosidodecahedron, and vice versa.