Conjucture About the Rhombic Penrose Tiling

Conjucture About the Rhombic Penrose Tiling

Roger Penrose is famous for many things, including the discovery of aperiodic tilings, the most familiar of which involves two types of rhombus:

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I think I have made a minor discovery about this Penrose tiling, and that is that one can add regular pentagons to it, in varying levels of pentagon-density, as shown in the first image, without it losing its aperiodicity. (I created only the first image, not the second.) I have not, however, proven this, and doubt I will.

Is this conjecture provable? I think so, but I lack the ability to write such a proof myself.

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