"Periodic Self-Dual Tilings"

Title: The Symmetry Pairings of Periodic Self-Dual Tilings

Authors: Brigitte Servatius and Herman Servatius

Reference: Preprint available after the Washington Exhibition

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 its group of isomorphisms and dualities consitits of isometries The most familiar example of a selfdual tiling is the tiling of the plane by squares. We give a catalogue of all symmetry pairings, together with examples and applications.