cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A331060 Coordination sequence for trivalent vertex in 1-skeleton of deltoidal hexecontahedron.

Original entry on oeis.org

1, 3, 6, 9, 12, 15, 12, 3, 1
Offset: 0

Views

Author

N. J. A. Sloane, Jan 08 2020

Keywords

Comments

Computed by Tom Karzes (see link).

Links

Crossrefs

Cf. A331061, A331062.

A331061 Coordination sequence for tetravalent vertex in 1-skeleton of deltoidal hexecontahedron.

Original entry on oeis.org

1, 4, 8, 12, 16, 14, 5, 2
Offset: 0

Views

Author

N. J. A. Sloane, Jan 08 2020

Keywords

Comments

Computed by Tom Karzes (see link).

Links

Crossrefs

Cf. A331060, A331062.

A331062 Coordination sequence for pentavalent vertex in 1-skeleton of deltoidal hexecontahedron.

Original entry on oeis.org

1, 5, 10, 15, 15, 10, 6
Offset: 0

Views

Author

N. J. A. Sloane, Jan 08 2020

Keywords

Comments

Computed by Tom Karzes (see link).

Links

Crossrefs

Cf. A331060, A331061.

A331065 Coordination sequence for first kind of trivalent vertex in 1-skeleton of pentagonal icositetrahedron.

Original entry on oeis.org

1, 3, 6, 9, 9, 6, 3, 1
Offset: 0

Views

Author

N. J. A. Sloane, Jan 08 2020

Keywords

Comments

Computed by Tom Karzes (see link).

Links

Crossrefs

Cf. A331066, A331067.

A331066 Coordination sequence for second kind of trivalent vertex in 1-skeleton of pentagonal icositetrahedron.

Original entry on oeis.org

1, 3, 7, 9, 8, 7, 3
Offset: 0

Views

Author

N. J. A. Sloane, Jan 08 2020

Keywords

Comments

Computed by Tom Karzes (see link).

Links

Crossrefs

Cf. A331065, A331067.

A331067 Coordination sequence for tetravalent vertex in 1-skeleton of pentagonal icositetrahedron.

Original entry on oeis.org

1, 4, 8, 8, 8, 8, 1
Offset: 0

Views

Author

N. J. A. Sloane, Jan 08 2020

Keywords

Comments

Computed by Tom Karzes (see link).

Links

Crossrefs

Cf. A331065, A331066.

A331068 Coordination sequence for first kind of trivalent vertex in 1-skeleton of pentagonal hexecontahedron.

Original entry on oeis.org

1, 3, 6, 12, 15, 12, 15, 18, 6, 3, 1
Offset: 0

Views

Author

N. J. A. Sloane, Jan 08 2020

Keywords

Comments

Computed by Tom Karzes (see link).

Links

Crossrefs

Cf. A331069, A331070.

A331069 Coordination sequence for second kind of trivalent vertex in 1-skeleton of pentagonal hexecontahedron.

Original entry on oeis.org

1, 3, 8, 12, 13, 16, 17, 12, 7, 3
Offset: 0

Views

Author

N. J. A. Sloane, Jan 08 2020

Keywords

Comments

Computed by Tom Karzes (see link).

Links

Crossrefs

Cf. A331068, A331070.

A331070 Coordination sequence for pentavalent vertex in 1-skeleton of pentagonal hexecontahedron.

Original entry on oeis.org

1, 5, 10, 10, 15, 20, 10, 10, 10, 1
Offset: 0

Views

Author

N. J. A. Sloane, Jan 08 2020

Keywords

Comments

Computed by Tom Karzes (see link).

Links

Crossrefs

Cf. A331068, A331069.

A162495 Number of reduced words of length n in the icosahedral reflection group [3,5] of order 120.

Original entry on oeis.org

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
Offset: 0

Views

Author

John Cannon and N. J. A. Sloane, Dec 01 2009

Keywords

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 PoincarĂ© polynomial.
  • David Wells, Archimedean polyhedra in Penguin Dictionary of Curious and Interesting Geometry, Penguin Books, 1991, pp. 6-7.

Links

Crossrefs

Cf. A161409, A162493, A162494, A162496, A162497.

Programs

  • Magma
    G := CoxeterGroup(GrpFPCox, "H3");
f := GrowthFunction(G);
Coefficients(f);

Formula

G.f.: (1-x^2)*(1-x^6)*(1-x^10)/(1-x)^3.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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