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It might not be obvious that these two forms have the same topology, but with a little stretching it’s possible to transform one into the other:pic.twitter.com/cCVJs3c4ub
On my list of 500 mathy things to do is to tesselate the flat version into a triangular mesh, glue the corresponding boundaries, and then try #DiscreteDifferentialGeometry curvature flow to get the final genus 3 surface, e.g. as in https://www.cs.cmu.edu/~kmcrane/Projects/ConformalWillmoreFlow/paper.pdf … by @keenanisalive et al.
You might also be interested in this paper... http://page.math.tu-berlin.de/~chern/projects/ShapeFromMetric/ …
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