Non-periodic rhomb substitution tilings that admit order n rotational symmetry

摘要

For each n is an element of N we construct a substitution rule using the set of rhombs with angles (pi k). These substitution rules generate a local isomorphism class of tilings closed under rotation of order 2n, and also admit singular tilings fixed under a rotation of order n. The scaling factors for this set of substitution rules includes algebraic numbers of every rank.