A method and system for forming a hexagonal woven fabric provide a hexagonal pattern loom including loom pins arranged in a hexagonal pattern to form a structure for engaging a continuous yarn strand. The loom pins form a top angled side of the hexagonal pattern and a bottom angled side of the hexagonal pattern. A set of the loom pins form two opposite straight sides of the hexagonal pattern forming the hexagonal pattern loom. A bias weaving process uses the continuous yarn strand for forming a top woven triangle fabric section, a bottom woven triangle fabric section, and a middle section of parallel yarn strand portions of the single continuous yarn strand. Traditional back-and-forth weaving uses the continuous yarn strand as weft strands in the middle section of parallel yarn strand portions for forming a rectangular woven fabric section. A hexagonal woven fabric uses the continuous yarn strand.