Abstract
If a planar lattice contains the vertices of a convex equilateral n-gon for some n≠4, then the lattice is similar to a sublattice of Z5 in R5, and it contains the vertices of a convex equilateral 2n-gon for every n≥2. If a planar lattice contains the vertices of an equilateral triangle, then the lattice is similar to a sublattice of Z3 in R3, and it contains the vertices of a convex equilateral n-gon for every n≥3.
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