Symmetry, automorphisms, and self-duality of infinite planar graphs and tilings

Title: Symmetry, automorphisms, and self-duality of infinite planar graphs and tilings (download pdf)

Authors: Brigitte Servatius and Herman Servatius

Reference: ``Proceedings of the Internatinal Geometry Conference in Zilina'', Vojtek Balint, Ed., 83-116, 1998.

Selected Figues|Abstract

Selected Figures:

Decorated Selfdual Tilings (Try inverting the colors!).
Selfdual tilings with CM as the duality group.
Selfdual tilings with CMM as the duality group.
Selfdual tilings with P2 as the duality group.
Selfdual tilings with P4 as the duality group.
Selfdual tilings with P4G as the duality group.
Selfdual tilings with P4M as the duality group.
Selfdual tilings with PG as the duality group.
Selfdual tilings with PGG as the duality group.
Selfdual tilings with PL as the duality group.
Selfdual tilings with PM as the duality group.
Selfdual tilings with PMM as the duality group.
Selfdual tilings with PMG as the duality group.

Abstract:

A tiling is geometrically self-dual, or harmoniously self-dual if itsgroup of isomorphisms and dualities consitits of isometries The most familiarexample of a selfdual tiling is the tiling of the plane by squares. We give a catalogue of all symmetry pairings, together with examples andapplications.