GEOMETRIC SYMMETRY IN PATTERNS AND TILINGS

By R. GIRIS

CONTENTS INTRODUCTION REFERENCES CLASSI?CATION OF DESIGNS BY SYMMETRY GROUP SYMMETRY AND ITS RELEVANCE TO DESIGNS SYMMETRY OPERATIONS SYMMETRY GROUP FIGURES AND DESIGNS CLASSI?CATION OF ?NITE DESIGNS STRUCTURE OF TRANSLATIONAL DESIGNS GENERATING FUNCTIONS CLASSI?CATION OF MONOTRANSLATIONAL DESIGNS 2 10 CLASSI?CATION OF DITRANSLATIONAL DESIGNS 2 11 CONSTRUCTION OF ?NITE DESIGNS 2 12 CONSTRUCTION OF MONOTRANSLATIONAL DESIGNS 2 13 CONSTRUCTION OF DITRANSLATIONAL DESIGNS 2 14 SUMMARY CLASSI?CATION OF DESIGNS BY SYMMETRY GROUP AND DESIGN UNIT NOTATION FINITE DESIGNS MONOTRANSLATIONAL DESIGNS DITRANSLATIONAL DESIGNS CONSTRUCTION OF ?NITE DESIGNS CONSTRUCTION OF MONOTRANSLATIONAL DESIGNS CONSTRUCTION OF DITRANSLATIONAL DESIGNS SUMMARY CLASSI?CATION OF DISCRETE PATTERNS MONOMOTIF PATTERN DISCRETE PATTERN PRIMITIVE PATTERN INDUCED MOTIF GROUPS MOTIF-TRANSITIVE SUBGROUPS CLASSI?CATION OF ?NITE DISCRETE PATTERN TYPES CLASSI?CATION OF MONOTRANSLATIONAL DISCRETE PATTERN TYPES CLASSI?CATION OF DITRANSLATIONAL DISCRETE PATTERN TYPES 4 10 CONSTRUCTION OF ?NITE PATTERN TYPES 4 11 CONSTRUCTION OF MONOTRANSLATIONAL DISCRETE PATTERN TYPES 4 12 CONSTRUCTION OF DITRANSLATIONAL DISCRETE PATTERN TYPES 4 13 SUMMARY