Lattices on simplicial partitions which are not simply connected

In this paper, (d+1)(d+1)-pencil lattices on simplicial partitions in RdRd, which are not simply connected, are studied. It is shown, how the fact that a partition is not simply connected can be used to increase the flexibility of a lattice. A local modification algorithm is developed also to deal with slight partition topology changes that may appear afterwards a lattice has already been constructed.