|
| |
|
|
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
|
Table of n, a(n) for n=0..101.
Tom Karzes, Polyhedron Coordination Sequences
Eric Weisstein's World of Mathematics, Great Rhombicosidodecahedron
Index entries for coordination sequences
|
|
|
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
|
| |
|
|
