Equilateral dimension of the planar Banach-Mazur compactum

We prove that there are arbitrarily large equilateral sets of planar and symmetric convex bodies in the Banach–Mazur distance. The order of the size of these d-equilateral sets asymptotically matches the bounds of the size of maximum-size d-separated sets (determined by Bronstein in 1978), showing that our construction is essentially optimal