PERFECT MATCHING RULES FOR UNDECORATED TRIANGULAR TILINGS WITH 10-, 12-, AND 8-FOLD SYMMETRY

Abstract

Perfect matching rules are derived for quasiperiodic triangular tilings with 10-, 12-, and 8-fold symmetry. We use the composition/decomposition approach via local inflation/deflation symmetry and emphasize the locality of our procedure: The matching rules given here are formulated using certain decorations of the tilings. These decorations turn out to be redundant, i.e., they are locally derivable from the undecorated tilings. Hence, the latter are determined by perfect matching rules as well.