We examine the substitution method for creating seven-fold quasiperiodic tilings with rhombi. From Ptolemy’s theorem, we obtain relations between the sides of the regular heptagon and its diagonals. This then gives us the length of diagonals of the rhombi and defines the possible inflation ratios. For a given inflation ratio, we obtain the numbers of the various small rhombi required to substitute the entire inflated rhombus tile as well as the rhombi at its border. For mirror symmetric substitutions, we also get the rhombus tiles at the mirror axis. A quasiperiodic tiling of seven-fold rotational symmetry is presented and examined with respect to these results. This approach could be used to create tilings of five-fold and other rotational symmetries.