The minimum diameter octagon with unit-length sides: Vinczeʹs wifeʹs octagon is suboptimal

This paper answers a query of Vincze (Acta Univ. Szeged, Sect. Sci. Math. 12 A (1950) 136–142): find the convex octagon with unit-length sides and minimum diameter. It also shows that the solution is ε-unique. The proof uses geometric arguments and a global optimization algorithm to solve a nonconvex quadratic program.