Triply Periodic Helical Weaves

Abstract

Weaving typically involves forming a sufrace by interlacing fibers into a mechanically stable arrangement, effectively making a two-dimensional object out of one-dimensional objects. Moorish Fretwork involves interweaving solid helical elements into mechanically stable two-dimensional arrangements by exploiting the helices' screw symmetry. A three-dimensional extension of this idea was demonstrated by Alexandru Usineviciu at Bridges in 2015. Here we expand the idea further by considering cases informed by invariant cylindrical rod packing, and cases related to geodesics of the gyroid. Simulations and/or physical models of nineteen triply periodic arrangements of interwoven helices are shown, with physical models demonstrated for eight.