Maloney's 7-fold

• Finite Local Complexity
• Finite Rotations
• Polytopal Tiles
• Self-Similar Substitution

Info

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

Patch

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References

[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

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