can distinguish between two cases. If the link at the centre of the star is timelike, the metric of the plane has Euclidean signature, all dihedral angles are Euclidean, and there are no further causality conditions to be satisfied. If on the other hand the link is spacelike, the orthogonal plane is Lorentzian, and so are the dihedral angles. Like in the 1+1 dimensional case discussed in the previous section, we must then require that there is exactly one pair of light cones at the central vertex, and that we encounter exactly four lightlike directions when circling around it. We say that the triangulation satisfies *link causality* if this condition is satisfied for every spacelike link.

Link causality guarantees that light cones everywhere in the triangulation are regular, except possibly at vertices. Intersecting the light cone(s) at a vertex $V$ with the surface of a unit ball around $V$, we obtain two disconnected circles if and only if local causality holds at $V$, see Fig. \[fig:vertexcausality\] (left). In terms of the triangulated surface $\cal S$ of the unit neighbourhood around $V$, vertex causality can be characterized as follows. Mark the end of a timelike link between $V$ and $\cal S$ 