The Nischke-Danzer-Deltoid 7-fold-2-2 was discussed and derived in [ND96] but not shown. A figure with the tiling can be found in [Pau2017] .

Polytopal Tiles Self Similar Substitution Finite Local Complexity Finite Rotations Nischke Danzer Deltoid

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 $n=7$.

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

The substitution tiling was derived from a mosaic at the Darb-i Imam Shrine in Isfahan, Iran. While the shrine dates back from 1453, [Lau2018] argues that the mosaic was created much later between 1715 - 1717. The tiling relies on the regular decagon and two hexagons and has individual dihedral symmetry ‘$D_{10}$‘. It was published in [LS2007] but the complete set of substitution rules can be found in [Ten2008] .

Finite Local Complexity Finite Rotations Polytopal Tiles Self Similar Substitution Girih

Tiling submitted by Andrew Hudson. The scaling factor is the smallest PV number, the Plastic Number which is a root of the polynomial $x^3 - x - 1 = 0$.

Self Similar Substitution Plastic Number Infinite Rotations