$E(x_{l-1},x_l)$ holds. In this case the sequence $(x_i,\ldots x_j)$ is called a *dense flag*. A *flag* is a sequence of vertices $(x_1,\ldots x_k)$ in which any two vertices are incident.

2.  The *residue* $R(x)$ of a vertex $x$ is the set of vertices incident with $x$.

3.  We say that two vertices $x$ and $y$ *intersect in the vertex* $z$ and write $z=x\wedge y$ if the set of vertices of type $V_0$ incident with $x$ and $y$ is exactly the set of vertices of type $V_0$ incident with $z$. If there is no vertex of type $V_0$ incident to $x$ and $y$, we say that $x$ and $y$ intersect in the empty set.

4.  We say that two vertices $x$ and $y$ *generate the vertex* $z$ and write $z=x\vee y$, if the set of vertices of type $V_n$ incident with $x$ and $y$ is exactly the set of vertices of type $V_n$ incident with $z$. If there is no vertex of type $V_n$ incident to $x$ and $y$, we say that $x$ and $y$ generate the empty set.

5.  A *simple cycle* is a cycle without repetitions.

We now give an inductive definition of a of dimension $n$:

A of 