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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, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, [1] great rhombicosidodecahedron, [2] [3] omnitruncated dodecahedron or omnitruncated icosahedron [4] is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.
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 ...
Ninth stellation of icosidodecahedron: I h: 56 Tenth stellation of icosidodecahedron: I h: 57 Eleventh stellation of icosidodecahedron: I h: 58 Twelfth stellation of icosidodecahedron: I h: 59 Thirteenth stellation of icosidodecahedron: I h: 60 Fourteenth stellation of icosidodecahedron: I h: 61 Compound of great stellated dodecahedron and ...
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 ]
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 ditrigonal icosidodecahedron (or great ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U 47. It has 32 faces (20 triangles and 12 pentagons ), 60 edges, and 20 vertices. [ 1 ]
A small complex icosidodecahedron can be constructed from a number of different vertex figures. A very similar figure emerges as a geometrical truncation of the great stellated dodecahedron , where the pentagram faces become doubly-wound pentagons ({5/2} --> {10/2}), making the internal pentagonal planes, and the three meeting at each vertex ...