# Carlo Séquin

I am a very visually oriented person. Geometry has been in my blood-stream since high-school. Formal proofs do not excite me until I can get some visualization model that supports that proof on an intuitive level. This is why I have been captivated by topics such as regular maps, graph embedding, or mathematical knots. Corresponding visualization models have led to geometrical sculptures that convey an aesthetic message even to people who do not know the mathematics underlying them. Conversely, abstract geometrical art-work by artists such as Brent Collins or Charles O. Perry have prompted me to discover the underlying mathematical principles and capture them in computer programs, which then produce more sculptures of the same kind.

This sculpture was inspired by Charles O. Perry’s 18-inch sand-cast sculpture called "Star Cinder," which is based on the icosahedral tangle of ten equatorial triangular loops. For my own sculpture, each original (3,1)-torus-knot loop has been replaced with a (3,3)-torus-knot, which corresponds to three mutually interlinked circles. Thus the whole configuration consists of a tangle of 30 circles – one each for every edge of an icosahedron. The challenge was to construct a single 2-manifold “soap-film” surface between those 30 border curves that retains the full symmetry of the oriented octahedron. The presented solution has three concentric, radially coupled shells, each with 20 triangular and 12 pentagonal openings.