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A211174
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Johannes Kepler's polyhedron circumscribing constant.
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2
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1, 4, 2, 5, 2, 3, 2, 9, 2, 1, 5, 0, 1, 1, 3, 5, 6, 3, 9, 3, 9, 0, 4, 6, 2, 1, 8, 8, 8, 5, 1, 1, 0, 8, 3, 2, 8, 6, 2, 0, 6, 6, 0, 8, 5, 8, 0, 9, 7, 7, 6, 1, 0, 8, 8, 9, 3, 7, 1, 5, 4, 8, 7, 4, 7, 8, 3, 1, 8, 7, 0, 0, 1, 5, 5, 5, 8, 5, 3, 5, 4, 3, 1, 6, 2, 1, 6, 2, 1, 9, 4, 7, 5, 4, 5, 7, 5, 7, 1, 5, 1, 6, 4, 6, 5, 5, 8, 4, 8, 7, 8
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OFFSET
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2,2
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COMMENTS
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The finite solid analogy to the plane polygon circumscribing constant (A051762).
The five Platonic solids are the tetrahedron, the hexahedron or cube, the octahedron, the dodecahedron and the icosahedron.
The geometric interpretation is as follows. Begin with a unit sphere. Circumscribe a tetrahedron and then circumscribe a sphere. Circumscribe a cube and then circumscribe a sphere. Circumscribe an octahedron and then circumscribe a sphere. Circumscribe a dodecahedron and then a sphere. Circumscribe an icosahedron and then a sphere. The constant is the radius of this last sphere. In actuality, it makes no difference the order of the five solids.
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LINKS
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FORMULA
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= 9*(15 - 6*sqrt(5)).
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EXAMPLE
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14.25232921501135639390462188851108328620660858097761088937154874783...
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MATHEMATICA
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RealDigits[ 9(15 - 6 * Sqrt[5]), 10, 111][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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