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The topology and symmetry group of a free boundary minimal surface in thethree-dimensional Euclidean unit ball do not determine the surface uniquely. Weprovide pairs of non-isometric free boundary minimal surfaces having anysufficiently large genus $g$, three boundary components and antiprismaticsymmetry group of order $4(g+1)$.

Infinitely many pairs of free boundary minimal surfaces with the same topology and symmetry group