Anon-realizable lopsided subset of the 7-cube

A lopsided set is a subset of the vertices of the n-cube that has a combinatorial property shared by the collection of orthants intersected by a convex subset of .The connection between lopsided sets and oriented matroids is exploited to obtain a lopsided subset of the 7-tube that cannot be realized as the collection of orthants intersected by a convex subset of