  In any spatially discrete model of pedestrian motion which uses a regular
lattice as basis, there is the question of how the symmetry between the
different directions of motion can be restored as far as possible but with
limited computational effort. This question is equivalent to the question ''How
important is the orientation of the axis of discretization for the result of
the simulation?'' An optimization in terms of symmetry can be combined with the
implementation of higher and heterogeniously distributed walking speeds by
representing different walking speeds via different amounts of cells an agent
may move during one round. Therefore all different possible neighborhoods for
speeds up to v = 10 (cells per round) will be examined for the amount of
deviation from radial symmetry. Simple criteria will be stated which will allow
find an optimal neighborhood for each speed. It will be shown that following
these criteria even the best mixture of steps in Moore and von Neumann
neighborhoods is unable to reproduce the optimal neighborhood for a speed as
low as 4.
