Schaad's 7-fold

Discovered by


Schaad’s 7-fold is a variation of Madison’s 7-Fold, hence it shares many properties with it. It allows for tilings with global 7-fold symmetry and a lot of locally 7-fold symmetric patches. There are three tile shapes, but only seven instead of nine different prototiles. The inflation factor is a PV number: $2+2\cos\left(\frac{\pi}{7}\right)+2\cos\left(\frac{2\pi}{7}\right) = 5.04891733952231\ldots$ which is the largest root of $x^{3}-6x^{2}+5x-1$.

Substitution Rule

Rule Schaad's 7-fold


Patch Schaad's 7-fold download vectorformat Schaad's 7-fold


P. Stampfli and T. P. Schaad
Ptolemy, the Regular Heptagon, and Quasiperiodic Tilings
Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture 2022, 39, 135-142, bridges2022-135.pdf