Sculptures which Stellarize Non-Planar Hexagons

Douglas G. Burkholder
Bridges Donostia: Mathematics, Music, Art, Architecture, Culture (2007)
Pages 343–350


In this paper we describe procedures for turning any random non-planar hexagon into five radically different sculptures that are mathematically interesting and esthetically pleasing. In each situation, we start by sketching a planar hexagon with relatively nice symmetries – noting that a regular hexagon is far too restrictive. We then describe a method for turning this sketch into a sequence of linear steps which, when applied to any non-planar hexagon will construct an affine image of our sketch. Since the resulting hexagon is affine, this process is mathematically interesting because it planarizes our non-planar hexagon. By adding motion to the hexagon that we sketch, we can add the sense of motion to the sculpture. This added motion provides unexpected results which can turn our sculptures into art.