Ob flat flag-transitive c.c*-geometries

We study Aat flag-transitive c.c*-geometries. We prove that, apart from one exception related to Sym(6), all these geometries are gluings in the meaning of [6]. They are obtained by gluing two copies of an affine space over GF(2). There are several ways of gluing two copies of the n-dimensional affine space over GF(2). In one way, which deserves to be called the canonical one, we get a geometry with automorphism group G = 2(2n) . L(n)(2) and covered by the truncated Coxeter complex of type D-2n. The non-canonical ways give us geometries with smaller automorphism group (G less than or equal to 2(2n) . (2(n)-1)(n)) and which seldom (never ?) can be obtained as quotients of truncated Coxeter complexes.