

A167227


Number of 2selfhedrites with n vertices.


2



1, 1, 2, 2, 3, 3, 3, 3, 5, 4, 4, 6, 5, 5, 8, 5, 6, 8, 6, 8, 10, 7, 7, 10, 10, 8, 12, 10, 9, 14, 9, 9, 14, 10, 14, 16, 11, 11, 16
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OFFSET

2,3


COMMENTS

From Table 2, p.11, of Sikiric. Number of 2selfhedrites with 4 <= n <= 40 and 2 <= i <= 4. An ihedrite is a 4regular plane graph with faces of size 2, 3 and 4. We do a short survey of their known properties and explain some new algorithms that allow their efficient enumeration. Using this we give the symmetry groups of all ihedrites and the minimal representative for each. We also review the link of 4hedrites with knot theory and the classification of 4hedrites with simple central circuits. An iselfhedrite is a selfdual plane graph with faces and vertices of size/degree 2, 3 and 4. We give a new efficient algorithm for enumerating them based on ihedrites. We give a classification of their possible symmetry groups and a classification of 4selfhedrites of symmetry T, Td in terms of the GoldbergCoxeter construction. Then we give a method for enumerating 4selfhedrites with simple zigzags.


LINKS

Table of n, a(n) for n=2..40.
Mathieu Dutour Sikiric, Michel Deza, 4regular and selfdual analogs of fullerenes, Oct 28, 2009.


CROSSREFS

Cf. A167156A167160, A167228, A167229.
Sequence in context: A284523 A034584 A035430 * A048280 A024695 A259195
Adjacent sequences: A167224 A167225 A167226 * A167228 A167229 A167230


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Oct 30 2009


STATUS

approved



