combinatorics – properties of identically auto-dual matroids

I'm dealing with a matroid M identical to the dual on the vertices E =[2N]In other words, if B is a base of M, E-B is also a base of M itself. I need simple combinatorial properties of these elements, such as the structure of the flats network, the properties of the basic circuits of the bases, and so on. Nothing important, but before you spend a lot of time there, does anyone know if I find this systematically done somewhere?