  The notion of "antimatroid with repetition" was conceived by Bjorner, Lovasz
and Shor in 1991 as a multiset extension of the notion of antimatroid. When the
underlying set consists of only two elements, such two-dimensional antimatroids
correspond to point sets in the plane. In this research we concentrate on
geometrical properties of antimatroidal point sets in the plane and prove that
these sets are exactly parallelogram polyominoes. Our results imply that
two-dimensional antimatroids have convex dimension 2. The second part of the
research is devoted to geometrical properties of three-dimensional antimatroids
closed under intersection.
