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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.
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In geometry, the elongated pentagonal gyrobirotunda or elongated icosidodecahedron is one of the Johnson solids (J 43).As the name suggests, it can be constructed by elongating a "pentagonal gyrobirotunda," or icosidodecahedron (one of the Archimedean solids), by inserting a decagonal prism between its congruent halves.
The intersection of both solids is the icosidodecahedron, and their convex hull is the rhombic triacontahedron. Seen from 2-fold, 3-fold and 5-fold symmetry axes The decagon on the right is the Petrie polygon of both solids.
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.
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 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.