A homotopy double groupoid of a hausdorff space

We associate to a Hausdorff space, X, a double groupoid, 2 (X), the homotopy double groupoid of X.The construction is based on the geometric notion of thin square.Under the equivalence of categories between small 2-categories and double categories with connection given in [BM] the homotopy double groupoid corresponds to the homotopy 2-groupoid, G 2 (X), constructed in [HKK].The cubical nature of 2 (X) as opposed to the globular nature of G 2 (X) should provide a convenient tool when handling 'local-to-global' problems as encountered in a generalised van Kampen theorem and dealing with tensor products and enrichments of the category of compactly generated Hausdorff spaces.