  In this paper, we consider the problem of formation of a series of geometric
patterns [4] by a network of oblivious mobile robots that communicate only
through vision. So far, the problem has been studied in models where robots are
either assumed to have distinct identifiers or to be completely anonymous. To
generalize these results and to better understand how anonymity affects the
computational power of robots, we study the problem in a new model, introduced
recently in [5], in which n robots may share up to 1 <= h <= n different
identifiers. We present necessary and sufficient conditions, relating
symmetricity and homonymy, that makes the problem solvable. We also show that
in the case where h = n, making the identifiers of robots invisible does not
limit their computational power. This contradicts a result of [4]. To present
our algorithms, we use a function that computes the Weber point for many
regular and symmetric configurations. This function is interesting in its own
right, since the problem of finding Weber points has been solved up to now for
only few other patterns.
