Given an integer n > 0, let f(n) denote the least dimension of the Euclidean space into which there exists an isometric embedding of **every** Riemannian flat n-dimensional torus T<sup>n</sup> = ℝ<sup>n</sup> / L, where L is an n-dimensional lattice in ℝ<sup>n</sup>. What is known about f(n) in terms of exact values, upper and lower bounds, or asymptotics?