Author:

Keywords:

negative curvature, chemical-structures, carbon allotropes, relevance, Science & Technology, Physical Sciences, Chemistry, Physical, Physics, Atomic, Molecular & Chemical, Chemistry, Physics, NEGATIVE CURVATURE, CHEMICAL-STRUCTURES, CARBON ALLOTROPES, RELEVANCE, 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics, 0306 Physical Chemistry (incl. Structural), 0307 Theoretical and Computational Chemistry, Chemical Physics, 3406 Physical chemistry, 3407 Theoretical and computational chemistry

Abstract:

The group of automorphisms of the 32-vertex Dyck graph is identified as the tetrakisoctahedral group; O-4. This group has 96 elements and conserves orientation on the standard embedding of the Dyck graph on a surface of genus 3, consisting of 12 octagons. An alternative regular map of the Dyck graph on a torus is found, which is made up of 16 hexagons. Orientation on this surface is conserved by another group of 96 elements, T-4(h), which is non-isomorphic to O-4. The subgroup structures of O-4 and T-4(h) are derived, and character tables of O-4 and some of its subgroups are constructed. The symmetry representations of the Dyck graph and its topological dual are determined. Finally a molecular realization of the Dyck graph on the genus-3 `Plumber's nightmare' is proposed, which can be considered as a new type of octagonal carbon network.