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A060296
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Number of regular convex polytopes in n-dimensional space, or -1 if the number is infinite.
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9
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1, 1, -1, 5, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET
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0,4
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REFERENCES
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H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973.
B. Grünbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.
P. McMullen and E. Schulte, Abstract Regular Polytopes, Encyclopedia of Mathematics and its Applications, Vol. 92, Cambridge University Press, Cambridge, 2002.
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LINKS
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Table of n, a(n) for n=0..112.
John Baez, Platonic Solids in All Dimensions, Nov 12 2006
Brady Haran, Pete McPartlan, and Carlo Sequin, Perfect Shapes in Higher Dimensions, Numberphile video (2016)
Index entries for linear recurrences with constant coefficients, signature (1).
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FORMULA
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a(n) = 3 for all n > 4. - Christian Schroeder, Nov 16 2015
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EXAMPLE
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a(2) = -1 because of the regular polygons in the plane.
a(3) = 5 because in R^3 the regular convex polytopes are the 5 Platonic solids.
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CROSSREFS
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Cf. A000943, A000944, A053016, A063927, A093478, A093479.
Sequence in context: A222466 A195448 A079267 * A114598 A272489 A259500
Adjacent sequences: A060293 A060294 A060295 * A060297 A060298 A060299
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KEYWORD
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sign,easy
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Mar 24 2001
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STATUS
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approved
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