The henomeric types of 2-sided patterns in the plane

Abstract

We extend the classification of pattern types by Grunbaum and Shephard to the 2-sided plane to include patterns having layered or interlaced motifs. Such patterns may have symmetries that turn the plane over. There are 17 infinite families of pattern types for 2-sided rosettes (twelve 1-parameter families and five 2-parameter families), 68 types of 2-sided frieze pattern, and 264 types of 2-sided periodic pattern. The definition of ‘henomeric’ is clarified to ensure that two of the periodic patterns are distinguished.