Sub Rosa n-fold

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

Info

J. Kari and M. Rissanen derived a set of rhomb substitution tilings in [KR2016] with n-fold dihedral symmetry.

• All substitution rules have dihedral $D_{2}$ symmetry.
• All edges of the substitution rules are equal and also have dihedral $D_{2}$ symmetry.
• All interior angles of all prototiles are integer multiples of $\frac{\pi}{n}$.

The minimal inflation facctor for this type of substitution tilings was discussed and derived in [Pau2017] .

The example shown below is the tiling for $n=7$.

Substitution Rule

Patch

download vectorformat Sub Rosa n-fold

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References

[Pau2017]
Pautze, S
Cyclotomic aperiodic substitution tilings
Symmetry 2017, 9(2), doi.org/10.3390/sym9020019

[KR2016]
Kari, J.; Rissanen, M.
Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry
Discrete Comput Geom 2016, 55, 972–996, https://doi.org/10.1007/s00454-016-9779-1

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