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 A162495 Number of reduced words of length n in the icosahedral reflection group [3,5] of order 120. 1
 1, 3, 5, 7, 9, 11, 12, 12, 12, 12, 11, 9, 7, 5, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This group is also the Weyl group H_3. If the 0's are omitted, this is the coordination sequence for the truncated icosidodecahedron (see Karzes link). Sometimes "great rhombicosidodecahedron" is preferred when referring in particular to the Archimedean polyhedron with this coordination sequence. - Peter Munn, Mar 22 2021 REFERENCES H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10. J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial. David Wells, Archimedean polyhedra in Penguin Dictionary of Curious and Interesting Geometry, Penguin Books, 1991, pp. 6-7. LINKS Tom Karzes, Polyhedron Coordination Sequences Eric Weisstein's World of Mathematics, Great Rhombicosidodecahedron FORMULA G.f.: (1-x^2)*(1-x^6)*(1-x^10)/(1-x)^3. PROG (Magma) G := CoxeterGroup(GrpFPCox, "H3"); f := GrowthFunction(G); Coefficients(f); CROSSREFS Cf. A161409, A162493, A162494, A162496, A162497. Sequence in context: A206544 A122799 A345425 * A107315 A340855 A230078 Adjacent sequences: A162492 A162493 A162494 * A162496 A162497 A162498 KEYWORD nonn,fini AUTHOR John Cannon and N. J. A. Sloane, Dec 01 2009 STATUS approved

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Last modified March 31 17:56 EDT 2023. Contains 361672 sequences. (Running on oeis4.)