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The truncated icosahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. [5] It has the same symmetry as the regular icosahedron, the icosahedral symmetry , and it also has the property of vertex-transitivity .
In geometry, the rectified truncated icosahedron is a convex polyhedron. It has 92 faces: 60 isosceles triangles , 12 regular pentagons , and 20 regular hexagons . It is constructed as a rectified , truncated icosahedron , rectification truncating vertices down to mid-edges.
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 rhombicosidodecahedron shares the vertex arrangement with the small stellated truncated dodecahedron, and with the uniform compounds of six or twelve pentagrammic prisms. The Zometool kits for making geodesic domes and other polyhedra use slotted balls as connectors. The balls are "expanded" rhombicosidodecahedra, with the squares replaced ...
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 ...
Small triambic icosahedron (First stellation of icosahedron) (Triakis icosahedron) I h: 27 Second stellation of icosahedron: I h: 28 Excavated dodecahedron (Third stellation of icosahedron) I h: 29 Fourth stellation of icosahedron: I h: 30 Fifth stellation of icosahedron: I h: 31 Sixth stellation of icosahedron: I h: 32 Seventh stellation of ...
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]
The truncated triakis icosahedron, or more precisely an order-10 truncated triakis icosahedron, is a convex polyhedron with 72 faces: 10 sets of 3 pentagons arranged in an icosahedral arrangement, with 12 decagons in the gaps.