Evolving Trefoil

Submitted by Carlo Sequin


Client: Missouri Western State University

Location: St. Joseph, MO, United States

Completion date: 2013

Project Team


Carlo H. Séquin

Industry Resource

David Lynn

Nova Blue Art Studios


“Evolving Trefoil” is a 10’ diameter sculpture made from fiber glass, epoxy, and polyester resins, serving as the focal point in a large 3-story atrium in a science building at MWSU. It consists of a twisted chain of 24 saddle/tunnel modules that are wound up into a trefoil knot.


This particular sculpture is a further evolutionary step in a series of collaborative pieces conceived by Brent Collins and Carlo Séquin involving chains of saddles and tunnels. This complex 3-dimensional structure looks quite different from different directions; it is ideally situated in a multi-story atrium, where it can be studied from many different stories and angles. The particular shape evokes many associations: The elaborate truss-like structure is reminiscent of the skeleton of a Cholla cactus; it thus celebrates engineering as much as the life sciences. The minimal surfaces spanning the saddle- and tunnel-elements like a soap film celebrate physics and chemistry. The overall shape represents a trefoil knot, the simplest mathematical knot. The twisted helical strands remind us of DNA and the molecular end of the life sciences, while the bleached off-white surfaces are reminiscent of Paleolithic bones.


"Evolving Trefoil" was a highly collaborative effort. It involved Brent Collins, who started in the 1990s to make use of the aesthetic elements emerging from the soap-film-like surface that forms a saddle-tunnel structure, which is known to mathematicians as Scherk’s Second Minimal Surface. Carlo Séquin then created a computer program that could generate such surfaces with saddles of higher order, incorporating twisting and non-uniform scaling along the Scherk-Collins chain. For this sculpture the program was enhanced so that the chain could wind along an arbitrary smooth space curve forming a trefoil knot. The overall shape was given a high degree of symmetry, so that only one sixth of the geometry is truly unique. This defining master geometry was carved full-size from high-density styro-foam on a numerically controlled milling machine. The result was then used by David Lynn at Nova Blue Studio Arts to make a complex multi-part mold, in which six replicas were constructed from fiber glass, epoxy, and polyester resins. The final assembly of the six 8’ long modules occurred on the floor of the atrium of Agenstein Hall in St. Joseph.