2009/10/28 by Mathieu Dutour Sikirić, Mathieu Dutour Sikiric, Sikiric, Mathieu Dutour +2
Chemistry · Materials Science · Mathematics · #Carbon Nanotubes in Composites #Combinatorics (math.CO) #FOS: Mathematics #Fullerene Chemistry and Applications #Geometric Topology (math.GT) #Graphene research and applications #math.CO #math.GT
paper · pdf · doi:10.48550/arxiv.0910.5323
16 pages, 14 figures
openalex publication_date 2009/10/28 · arxiv created 2009/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.