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A geodesic grid is a global Earth spatial reference that uses polygon tiles based on the subdivision of a polyhedron (usually the icosahedron, and usually a Class I subdivision) to subdivide the surface of the Earth.
For example, the icosahedron is {3,5+} 1,0, and pentakis dodecahedron, {3,5+} 1,1 is seen as a regular dodecahedron with pentagonal faces divided into 5 triangles. The primary face of the subdivision is called a principal polyhedral triangle (PPT) or the breakdown structure. Calculating a single PPT allows the entire figure to be created.
In geometry, the pentakis icosidodecahedron or subdivided icosahedron is a convex polyhedron with 80 triangular faces, 120 edges, and 42 vertices. It is a dual of the truncated rhombic triacontahedron ( chamfered dodecahedron ).
In geometry, the 31 great circles of the spherical icosahedron is an arrangement of 31 great circles in icosahedral symmetry. [1] It was first identified by Buckminster Fuller and is used in construction of geodesic domes .
As it turns out, the icosahedron occupies less of the sphere's volume (60.54%) than the dodecahedron (66.49%). [12] The dihedral angle of a regular icosahedron can be calculated by adding the angle of pentagonal pyramids with regular faces and a pentagonal antiprism. The dihedral angle of a pentagonal antiprism and pentagonal pyramid between ...
Loop subdivision of an icosahedron; refinement steps zero, one, and two. In computer graphics, the Loop method for subdivision surfaces is an approximating subdivision scheme developed by Charles Loop in 1987 for triangular meshes. Prior methods, namely Catmull-Clark and Doo-Sabin (1978), focused on quad meshes.
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Fuller (1975) used these 6 great circles, along with 15 and 10 others in two other polyhedra to define his 31 great circles of the spherical icosahedron. [ 6 ] The long radius (center to vertex) of the icosidodecahedron is in the golden ratio to its edge length; thus its radius is φ if its edge length is 1, and its edge length is 1 / φ ...
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