  Based on Monte-Carlo simulations, the stable magnetization configurations of
an antiferromagnet on a quasiperiodic tiling are derived theoretically. The
exchange coupling is assumed to decrease exponentially with the distance
between magnetic moments. It is demonstrated that the superposition of
geometric frustration with the quasiperiodic ordering leads to a
three-dimensional noncollinear antiferromagnetic spin structure. The structure
can be divided into several ordered interpenetrating magnetic supertilings of
different energy and characteristic wave vector. The number and the symmetry of
subtilings depend on the quasiperiodic ordering of atoms.
