Let \(s\in\mathbb{N}\) and \(0\leq a< b\), and let \(K\) be the union of line segments \(\bigcup^{s-1}_{k=0} e^{2\pi ik/s}[a, b]\). The author shows that the logarithmic capacity of \(K\) is given by \(((b^s- a^s)/4)^{1/s}\). As an application he deduces a saturation result concerning approximation by polynomials with integer coefficients. More precisely, let \(\mathbb{P}^I_n\) denote the collection of all polynomials of degree at most \(n\) with integer coefficients. Also, given \(f\in C(K)\), let \(E^I_n(f, K)= \inf_P\| f- P\|\), where the infimum is over all \(P\in \mathbb{P}^I_n\) and \(\| \cdot \|\) denotes the supremum norm over \(K\). It is shown that, if \(b^s- a^s< 1\) and \(\sum_n (4/(b^s- a^s))^{n/s}E^I_n(f, K)\) converges, then \(f\in \mathbb{P}^I_n\).