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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 most familiar spherical polyhedron is the soccer ball, thought of as a spherical truncated icosahedron. The next most popular spherical polyhedron is the beach ball, thought of as a hosohedron. Some "improper" polyhedra, such as hosohedra and their duals, dihedra, exist as spherical polyhedra, but their flat-faced analogs are degenerate.
In geometry, the chamfered truncated icosahedron is a convex polyhedron with 240 vertices, 360 edges, and 122 faces, 110 hexagons and 12 pentagons. It is constructed by a chamfer operation to the truncated icosahedron , adding new hexagons in place of original edges.
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 truncated icosahedron is a convex polyhedron constructed as an augmented truncated icosahedron, adding pyramids to the 12 pentagonal faces, creating 60 new triangular faces. It is geometrically similar to the icosahedron where the 20 triangular faces are subdivided with a central hexagon, and 3 corner triangles.
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.