  In this paper we prove the existence of quasiperiodic rhombic substitution
tilings with 2n-fold rotational symmetry, for any n. The tilings are
edge-to-edge and use [n/2] rhombic prototiles with unit length sides. We
explicitly describe the substitution rule for the edges of the rhombuses, and
prove the existence of the corresponding tile substitutions by proving that the
interior can be tiled consistently with the given edge substitutions.
