A coliniation is a permutation group that carries subsets of points to other subsets of points. The name coliniation is related to the word colinear, where the predefined subsets all contain two points. Each permutation carries pairs of points to other pairs of points, hence lines to lines. Each graph determines a coliniation.
Consider a regular n-gon. A permutation begins by mapping one vertex onto any other vertex in the n-gon. But lines must map to lines, so the adjacent vertex must map to a vertex that is adjacent to the image of the first. This continues as we work our way around the n-gon. The coliniation is Dn, as described earlier.