Symmetry groups of the Batak basketweave patterns

Layer groups are three-dimensional crystallographic groups that have translational symmetries in two dimensions. This paper discusses the layer group symmetries of the patterns arising from two-way twofold weaves found in the baskets, trays and mats of the Batak, an indigenous community in the Philippines. This study reports 44 distinct Batak weave patterns, culled from existing studies on Batak basketry; from museums, exhibits and social enterprises focusing on Batak products in the Philippines; and from a two-day visit to a Batak community in Palawan. The method used in this study to determine the symmetry group of a two-way twofold weave was to first codify the weave by means of a design, which is a 2-coloring of a regular tiling by squares where a tile is colored one of two colors, depending on whether a weft is over a warp or vice versa in the corresponding weave. Next, the side-preserving and side-reversing symmetries of the weave were derived from the color symmetry group structure of its corresponding design. The symmetry groups found are of 15 layer group types, out of the 80 layer groups known in crystallography.