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To a generic configuration of eight points in convex position in the plane,we associate a list consisting of the following information: for all of the 56conics determined by five of the points, we specify the position of eachremaining point, inside or outside. We prove that the number of possible lists,up to the action of $D_8$ on the set of points, is 47, and we give two possibleways of encoding these lists. A generic compex pencil of cubics has twelvesingular (nodal) cubics and nine distinct base points, any eight of themdetermine the ninth one, hence the pencil. If the base points are real, exactlyeight of these singular cubics are distinguished, that is to say real with aloop containing some base points. We call combinatorial cubic a topologicaltype (cubic, base points), and combinatorial pencil the sequence of eightsuccessive combinatorial distinguished cubics. Let us choose representants ofthe 47 orbits. In most cases, but four exceptions, a list determines a uniquecombinatorial pencil. We give a complete classification of the combinatorialpencils of cubics with eight base points in convex position. Up to the actionof $D_8$ on the set of points, there are $43$ such pencils.

Pencils of cubics with eight base points lying in convex position in $\mathbb{R}P^2$