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A198861
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The number of ways to paint the faces of the five Platonic solids using exactly n colors where n is the number of faces of each solid.
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3
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OFFSET
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1,1
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COMMENTS
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Let G, the group of rotations in 3 dimensional space act on the set of n! paintings of each Platonic solid having n faces. There are n! fixed points in the action table since the only element in G that leaves a painting fixed is the identity element. The order of G is A098427/2. So by Burnside's Lemma a(n)=n!/|G|.
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LINKS
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FORMULA
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PROG
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(PARI) lista() = {ve = [6, 12, 12, 30, 30 ]; vf = [4, 6, 8, 12, 20 ]; for (i=1, 5, nb = vf[i]!/(2*ve[i]); print1(nb, ", "); ); } \\ Michel Marcus, Aug 25 2014
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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