TWIN TREES AND LAMBDA(LAMBDA)-GONS

We define a natural generalization of generalized n-gons to the case o f Lambda-graphs (where Lambda is a totally ordered abelian group and 0 < lambda epsilon Lambda). We term these objects lambda(Lambda)-gons. We then show that twin trees as defined by Ronan and Tits can be viewe d as (1,0)(Lambda)-gons, where Lambda = Z x Z is ordered lexicographic ally. This allows us to then generalize twin trees to the case of Lamb da-trees. Finally, we give a free construction of lambda(Lambda)-gons in the cases where Lambda is discrete and has a subgroup bf index 2 th at does not contain the minimal element of Lambda.