  We study geometries that arise from the natural $G_2(K)$ action on the
geometry of one-dimensional subspaces, of nonsingular two-dimensional
subspaces, and of nonsingular three-dimensional subspaces of the building
geometry of type $C_3(K)$ where $K$ is a perfect field of characteristic 2. One
of these geometries is intransitive in such a way that the non-standard
geometric covering theory by the first and the last author is not applicable.
In this paper we introduce the concept of fused amalgams in order to extend the
geometric covering theory so that it applies to that geometry. This yields an
interesting new amalgamation result for the group $G_2(K)$.
