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Rectified Truncated Icosahedron
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 rectification (geometry), rectified, truncated icosahedron, rectification truncating vertices down to mid-edges. As a near-miss Johnson solid, under icosahedral symmetry, the pentagons are always regular, although the hexagons, while having equal edge lengths, do not have the same edge lengths with the pentagons, having slightly different but alternating angles, causing the triangles to be Isosceles triangle, isosceles instead. The shape is a symmetrohedron with notation ''I(1,2,*,[2])'' Images Dual By Conway polyhedron notation, the dual polyhedron can be called a ''joined truncated icosahedron'', jtI, but it is topologically equivalent to the rhombic enneacontahedron with all rhombic faces. Related polyhedra The ''rectified truncated icosahedron'' can be seen in sequence of rectification (geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Near-miss Johnson Solid
In geometry, a near-miss Johnson solid is a strictly convex set, convex polyhedron whose face (geometry), faces are close to being regular polygons but some or all of which are not precisely regular. Thus, it fails to meet the definition of a Johnson solid, a polyhedron whose faces are all regular, though it "can often be physically constructed without noticing the discrepancy" between its regular and irregular faces.. The precise number of near-misses depends on how closely the faces of such a polyhedron are required to approximate regular polygons. Some near-misses with high symmetry are also symmetrohedron, symmetrohedra with some truly regular polygon faces. Some near-misses are also zonohedron, zonohedra. Examples Coplanar misses Some failed Johnson solid candidates have coplanar faces. These polyhedra can be perturbed to become convex with faces that are arbitrarily close to regular polygons. These cases use 4.4.4.4 vertex figures of the square tiling, 3.3.3.3.3.3 vertex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
