  We consider the line planning problem in public transport in the Parametric
City, an idealized model that captures typical scenarios by a (small) number of
parameters. The Parametric City is rotation symmetric, but optimal line plans
are not always symmetric. This raises the question to quantify the symmetry gap
between the best symmetric and the overall best solution. For our analysis, we
formulate the line planning problem as a mixed integer linear program, that can
be solved in polynomial time if the solutions are forced to be symmetric. The
symmetry gap is provably small when a specific Parametric City parameter is
fixed, and we give an approximation algorithm for line planning in the
Parametric City in this case. While the symmetry gap can be arbitrarily large
in general, we show that symmetric line plans are a good choice in most
practical situations.
