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?