# Presentation of the Rybnikov matroid

In this well celebrated work Gregory Rybnikov exhibit an example of two arrangements with the same underlying matroid, but with fundamental groups which are not isomorphic. This is a key counterexample in hyperplane arrangement theory. In particular, this implies that the topology of the complement manifold of a hyperplane arrangement is not determined by the combinatorics of its lattice of intersections, i.e, its underlying matroid.

I am interested in some SageMath computations and I like to know an explicit presentation of the matroid introduced by Rybnikov. Maybe this matroid is already available in the SageMath library.

$\textbf{Question:}$ What are the ground set, the rank and the bases set $\mathfrak{B}$ of the Rybnikov matroid?