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.

[GKR2015]

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,
https://doi.org/10.1007/s00454-014-9659-5