Lawson's minimal surface of genus 2

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Lawson's minimal surface of genus 2
Geometry file (.stl format) for the 3D print of the Lawson surface, not set to scale.

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Nicholas Schmitt, Wjatscheslaw Kewlin

This 3D print shows the Lawson surface which is the only known example of a minimal surface of genus 2, i. e., with 2 holes, in the 3-dimensional sphere.

This 3D print shows the Lawson surface which is the only known example of a minimal surface of genus 2 in the 3-dimensional sphere. It was constructed by Lawson in 1970 using reflections and rotations of a fundamental piece, obtained by the solution of the Plateau problem. Recent progress in surface theory by Sebastian Heller and Nicholas Schmitt using Hitchin abelianization made it possible to conformally parametrize the surface. The parameter lines on the print show asymptotic lines of the surface in the 3-sphere, i. e., where the normal curvature vanishes.