  We construct the type-preserving panel-regular lattices in buildings of type
M, for M with entries two, three or infinity, which have cyclic stabilizers of
spherical 2-residues. We obtain these lattices as fundamental groups of their
associated quotient buildings, which are constructed by amalgamating quotients
of generalized digons and triangles by actions of Singer cyclic groups. Each
quotient construction has an associated gluing matrix which encodes how the
quotient generalized polygons are amalgamated. We show that these gluing
matrices also encode presentations of the panel-regular lattices.
