The structure of 4-flowers of vertically 4-connected matroids

Aikin and Oxley (2012) [2] studied the structure of 4-flowers in 4-connected matroids. In the paper we consider 4-flowers in vertically 4-connected matroids. There is a natural relation of equivalence on such 4-flowers. We characterize the structure that arises when 4-flowers are equivalent under the relation.