Leapfrog and Related Operations on Toroidal Fullerenes

Abstract

A 4-valent square tiled toroid is transformed into 3-valent hexagonal (and other polygonal) lat-tices either by simple cutting procedures or by some more elaborated operations such as leap-frog and related transformations. Tiling or embedding isomers can be interchanged by means of such operations on toroidal maps, for which rigorous definitions and some theorems are given. Parents and products of most important operations are illustrated. Key words carbon allotropes toroids 4-valent square tilings 3-valent hexagonal tilings leapfrog transformation * Author to whom correspondence should be addressed. (E-mail: