My thesis presents an ancient form of weaving knowledge known as triaxial bias plaited basketry. Informed by forty- plus years of studio practice my research investigates this advanced technique that uses three elements, woven at sixty degrees from each other, in a closed hexagonal structure. The technique presently is not widely known or practised; triaxial bias plaited basketry is in danger of extinction. My research asks: How can triaxial bias plaited basketry be preserved, and what approaches can be taken to help understand the complexity of its construction and pattern for future weavers? Drawing together written and visual resources, I first compile a body of historical knowledge, then apply an inductive mathematical theory of Making with Rigour: MathWeave to conduct an evidence-based approach toward research-creation methods. Key design elements of colour and weave techniques are fundamental to weaving, yet a critical gap in the knowledge of triaxial bias plaited basketry was made evident in the initial research. Responding to this knowledge gap, a practice-based research method was undertaken to document the creation of 52 experimental baskets, proposing new knowledge of colour placement pattern control and weave techniques. This research provides applied math and colour theory with advanced weaving knowledge, encouraging current and future basket makers to participate in triaxial bias plaited basketry, working toward the preservation of this technology.