Oriented matroids are combinatorial objects, which are a combinatorial abstraction of various objects such as point configurations, polytopes and hyperplane arrangements. One of the most outstanding results in oriented matroid theory is the Topological Representation Theorem, which asserts that every oriented matroid of rank r can be represented as a pseudosphere arrangement on the (r - 1) -dimensional sphere, By this theorem, matroid polytopes of rank 4, a special class of oriented matroids of rank 4, can be represented as a pseudosphere arrangement on the 3-dimensional sphere. In this paper, we provide a lower-dimensional version of Topological Representation Theorem for matroid polytopes of rank 4. We show that there is a one-to-one correspondence between matroid polytopes of rank 4 and certain topological objects in the 2-dimensional Euclidean space, which we call configurations of points and pseudocircles.
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