Geodesic
On flat flag-transitive $c.c\sp*$-geometries
Journal of Algebraic Combinatorics, Tome 6 (1997) no. 1, pp. 5-26.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study flat 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 $G = 2 ^{2 n }; L _{ n(2)}$ and covered by the truncated Coxeter complex of type $D _{2} ^{ n }$. The non-canonical ways give us geometries with smaller automorphism group $( Gle2 ^{2 n }; (2 ^{ n-1}) n)$ and which seldom (never ?) can be obtained as quotients of truncated Coxeter complexes.
Keywords: diagram geometry, semi-biplane, amalgam of group 
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     title = {On flat flag-transitive $c.c\sp*$-geometries},
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Baumeister, Barbara; Pasini, Antonio. On flat flag-transitive $c.c\sp*$-geometries. Journal of Algebraic Combinatorics, Tome 6 (1997) no. 1, pp. 5-26. http://geodesic.mathdoc.fr/item/JAC_1997__6_1_a4/