Bridges 2026 Exhibition of Mathematical Art, Craft, and Design

James Mallos

Artists

James Mallos

Sculptor

Washington, District of Columbia, USA

jbmallos@gmail.com

weaveanything.blogspot.com

View exhibition history

Statement

I am interested in simple descriptions of surfaces and shapes. In this work I am interested in making baskets from Gauss codes, a classical encoding of the crossings in a closed, self-crossing curve on the sphere. For simplicity of description, it is best to make a basket from single closed strand; such a basket is, mathematically speaking, a knot. Trigonal knots are associated with triangulations, and thus, potentially, with deltahedra (polyhedra faced with equilateral triangles). Where such an associated deltahedron exists, it can be realized by a loop of equilateral triangles that triply covers the surface, reminiscent of the "mad weave" or anyam gila weaving technique.

Artworks

Image for entry 'Three Unknots in the Shape of Deltahedra'

Three Unknots in the Shape of Deltahedra

10.0 x 40.0 x 40.0 cm

Computer-cut cardstock

2026

Additional info

These three baskets were made from strips of paper cardstock, cut, scored, and sequentially numbered by a Cricut Maker 4. The circular holes allow the Gauss code to be read off the finished basket. Each fold has two numbers, collecting those numbers as ordered pairs, and arranging the pairs in lowest-high-number order, recovers the code that told the weaver how to make the basket. The elliptical holes are slots that receive tabs holding each crossing in place. There is no actual weaving involved: the knot is built "over, over, over" in the manner of an ascending knot, so the resulting basket is, in fact, an unknot, but the tabs and the tight wrapping of the strip hold the basket together securely.