Hexagons are an obvious shape in the best known trixial basket structure, kagome, which is why it is often called hexagonal open weave, but actually triangles are more fundamental to its structure. This suggests the use of deltahedra as patterns for a wide variety of baskets, some having no hexagons at all. Some of them are closely related to Turk’s head knots and relationships to other fibre arts, knotting and braiding, are discussed. Some new decorative knots are described.