Maloney's 7-fold

Discovered by


A substitution for three triangular prototiles, based on 7-fold symmetry. The lengths of the edges of the tiles are $\sin(\frac{\pi}{7})$, $\sin(\frac{2\pi}{7})$, $\sin(\frac{3\pi}{7})$. These tilings are essentially different from Danzer’s 7-fold examples, see for instance Danzer’s 7-fold.

Substitution Rule

Rule Maloney's 7-fold


Patch Maloney's 7-fold


Gaehler, F. and Kwan, E.E. and Maloney, G.R.
A computer search for planar substitution tilings with n-fold rotational symmetry.
Discret. Comput. Geom. 2015, 53, pp. 445--465,