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%I #18 Jun 16 2018 22:08:43
%S 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,
%T 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,
%U 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
%N Number of regular convex polytopes in n-dimensional space, or -1 if the number is infinite.
%D H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973.
%D B. Grünbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.
%D P. McMullen and E. Schulte, Abstract Regular Polytopes, Encyclopedia of Mathematics and its Applications, Vol. 92, Cambridge University Press, Cambridge, 2002.
%H John Baez, <a href="http://math.ucr.edu/home/baez/platonic.html">Platonic Solids in All Dimensions</a>, Nov 12 2006
%H Brady Haran, Pete McPartlan, and Carlo Sequin, <a href="https://www.youtube.com/watch?v=2s4TqVAbfz4">Perfect Shapes in Higher Dimensions</a>, Numberphile video (2016)
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F a(n) = 3 for all n > 4. - _Christian Schroeder_, Nov 16 2015
%e a(2) = -1 because of the regular polygons in the plane.
%e a(3) = 5 because in R^3 the regular convex polytopes are the 5 Platonic solids.
%Y Cf. A000943, A000944, A053016, A063927, A093478, A093479.
%K sign,easy
%O 0,4
%A Ahmed Fares (ahmedfares(AT)my-deja.com), Mar 24 2001