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Proceedings of CAD'16, 2016, 39-43
Parametric Co-Design of Modular Free-Form 2-Manifolds
Abstract. For the Exhibition of Mathematical Art at the Joint Mathematics Meeting 2016 I wanted to create a couple of sculptures that could serve as mathematical visualization models for non-orientable surfaces of higher genus, but would also hold up as aesthetically pleasing free-form sculptures in their own right. Inspired by project LEGO-Knots, I planned to design a small set of modular components that could be assembled in many diverse ways to form single-sided (σ=1) as well as double-sided (σ=2) 2-manifolds of genus 2 and higher. The parts should be suitable for being built with Fused Deposition Modeling (FDM) or with Selective Laser Sintering (SLS), and they should result in sculptures that are about 1-2 feet tall.
Keywords. Tubular building blocks; fused-deposition modeling; Klein-bottles; non-orientable surfaces.