Naslov
4-regular and self-dual analogs of fullerenes

Autori
Dutour Sikirić, Mathieu ; Deza, Michel

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
The Mathematics and Topology of Fullerenes

Urednik/ci
Cataldo, Franco ; Graovac, Ante ; Ori, Ottorino

Izdavač
Springer

Grad
Berlin

Godina
2011

Raspon stranica
103-116

ISBN
978-94-007-0220-2

Ključne riječi
self-dual map, enumeration, groups, central circuit

Sažetak
An i-hedrite is a 4-regular 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 i-hedrites and the minimal representative for each. We also review the link of 4-hedrites with knot theory and the classification of 4-hedrites with simple central circuits. An i-self-hedrite is a self-dual plane graph with faces and vertices of size/degree 2, 3 and 4. We give a new efficient algorithm for enumerating them based on i-hedrites. We give a classification of their possible symmetry groups and a classification of 4-self-hedrites of symmetry T, Td in terms of the Goldberg-Coxeter construction. Then we give a method for enumerating 4-self-hedrites with simple zigzags.

Izvorni jezik
Engleski

Znanstvena područja
Kemija

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