Locally s-arc transitive graphs with two different quasiprimitive actions

Previous work of the authors has shown that an important class of locally (G,2)-arc transitive graphs are those for which G acts faithfully and quasiprimitively on each of its two orbits on vertices. In this paper we give a complete classification in the case where the two quasiprimitive actions of G are of different types. The graphs obtained have amalgams previously unknown to the authors and involve both an almost simple 2-transitive action and an affine 2-transitive action on the neighbourhoods of vertices.