# Paul Gailiunas

I have participated in every Bridges conference since 2000, and exhibited artwork since 2007, usually related to my conference presentation. I am interested in any visually interesting manifestation of mathematics, and have used a variety of media at various times: paper or card models, geometrical drawings, computer images, and I have used mathematically inspired designs in leather bookbindings. The use of basketry is fairly new to me, although I have played with one or two ideas over the years.

A mad weave tetrahedron woven from six strands. The constraints implied by the symmetry of the tetrahedron and the geometry of skew mad weave limit the possibilities of colour symmetry. In this example the first impression is of a random pattern, and the symmetries only become apparent after careful study.

A mad weave tetrahedron created using only three strands. If the strands in a basketry polyhedron are skewed relative to the edges they will follow quite complicated paths in general, but in the case of the tetrahedron they maintain a (more or less) constant direction, taking an approximately helical path between pairs of opposite edges. This means that it is possible to weave tetrahedra with only three strands.

A hexagonal antiprism created in basketry. The underlying structure is an open hexagonal framework made from two strands of plastic strapping (one green, one red). The framework has been filled-in by weaving two red strands parallel to the green and two green strands parallel to the red to complete a mad weave basket. Hexagonal weaves are chiral, inducing a marked chirality in the colouring of the polyhedral basket, most obviously in the helical patterning of the sides.