  We introduce a new practical and more general definition of local
symmetry-preserving operations on polyhedra. These can be applied to arbitrary
plane graphs and result in plane graphs with the same symmetry. With some
additional properties we can restrict the connectivity, e.g. when we only want
to consider polyhedra. Using some base structures and a list of 10 extensions,
we can generate all possible local symmetry-preserving operations
isomorph-free.
