Madison's 7-fold

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

Info

A tiling with 7-fold symmetry and a lot of locally 7-fold symmetric patches. There are only three tile shapes, but 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

Patch

download vectorformat Madison's 7-fold

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References

[Mad2018]
Madison, A.E.
Constructing Penrose-like tilings with 7-fold symmetry
Structural Chemistry 2018, 29, 645--655, 10.1007/s

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