Skyline queries represent a dataset by the points on its pareto frontier, but can become very large. To alleviate this problem, representative skylines select exactly k skyline points. However, existing approaches are not scaleinvariant, not stable, or must materialise the entire skyline. We introduce the maximum coverage representative skyline, which returns the k points collectively dominating the largest area of the data space. It satisfies the above properties and reflects a critical property of the skyline itself.