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math.MG2026
A note on Kuperberg's quadrilateral conjecture
Viktor Vígh
Kuperberg conjectured in 1983 that every convex body in the plane is contained in a quadrilateral of area at most , the extremal bodies being the affine-…
math.MG2026
A second eight-faced polyhedron in which every two faces share an edge
Gergely Röst, Viktor Vígh
We report a novel polyhedral surface of genus~3 embedded in with eight planar, simple, non-convex nonagonal faces, 24 vertices and 36 edges, in which every two faces…