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We introduce order-k @a-hulls and @a-shapes - generalizations of @a-hulls and @a-shapes. Being also a generalization of k-hull (known in statistics as ''k-depth contour''), order-k @a-hull provides a link between shape reconstruction and statistical depth. As a generalization of @a-hull, order-k @a-hull gives a robust shape estimation by ignoring locally up to k outliers in a point set. Order-k@a-shape produces an ''inner'' shape of the set, with the amount of ''digging'' into the points controlled by k. As a generalization of k-hull, order-k @a-hull is capable of determining ''deep'' points amidst samples from a multimodal distribution: it correctly identifies points which lie outside clusters of samples. The order-k @a-hulls and @a-shapes are related to order-k Voronoi diagrams in the same way in which @a-hulls and @a-shapes are related to Voronoi diagrams. This implies that order-k @a-hull and @a-shape can be readily built from order-k Voronoi diagram, and that the number of different order-k@a-shapes for all possible values of @a is proportional to the complexity of order-k Voronoi diagram.