are *adjacent* and write $k\adjac l$ if they intersect in a point from $S$. We say that three pairwise distinct points $a_1, a_2, a_3\in S$ (or lines $k_1, k_2, k_3\in\lines$) form a *triangle* in $\A$ if they are pairwise adjacent and not collinear (or not concurrent respectively), which we write as $\triangle(a_1, a_2, a_3)$ (or $\triangle(k_1, k_2, k_3)$ respectively). The points $a_1, a_2, a_3$ are called vertices and the lines $k_1, k_2, k_3$ are called sides of the triangle. A *subspace* of $\A$ is any set $X\subseteq S$ with the property that every line which shares with $X$ two or more points is entirely contained in $X$. We say that a subspace $X$ of $\A$ is *strong* if any two points in $X$ are collinear. If $S$ is strong then $\A$ is said to be a *linear space*.

Complements
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Let us fix a subset $\W\subset S$. By the *complement of $\W$ in $\A$* we mean the structure $$\fixoutf(\A,\W) := \struct{\pointsout, \linesout},$$ where $$\pointsout := S\setminus\W \qquad\text{and}\qquad
     \linesout := \{ k\in\lines\colon k\nsubseteq\W\}.$$ Here, the incidence relation is again $\in$, inherited from $\A$, but limited to the new point set and line set. It should not lead to confusion, as it 