Print-It-Yourself Puzzles

Currently Playing: Penrose Morph - If the outer rim of a Penrose tiling is given, is the solution then always a unique?

Print it yourself at https://oskarvandeventer.nl/Print-It-Yourself/. Buy at https://puzzleguy.store/products/penrose-morph-the-most-beautiful-packing-puzzle Penrose Morph is based on the famous non-periodical Penrose Tiling. This exists in several variations, amount others "kites and darts" and "acute and obtuse rhombuses". Craig Kaplan showed that here is a continuous morph between the dart and the obtuse rhombus, and also one between the kite and the accute+obtuse rhombus combined. In our first prototype, we used straight-line morphs between the two types of shapes. Alas, that morph does not enforce the aperiodicity of the tiling. So Craig modified the middle parts of the morph such that aperiodicity is enforced. As an aesthetic choice, the decahedral tiling of kites and darts was selected for the puzzle. Here is a fundamental mathematical question: if the outer edges of a subsection of the Penrose tiling are given (as in this puzzle), is then the inner tiling always univocal? Copyright (c) 2025, M. Oskar van Deventer. Frequently Asked Question: http://oskarvandeventer.nl/FAQ.html Buy mass-produced Oskar puzzles at https://www.puzzlemaster.ca/browse/inventors/oskar/ (USA, CA) and https://www.sloyd.fi/brain-teasers/inventors-designers/oskar-van-deventer (EU) Buy exclusive 3D-printed Oskar puzzles at https://i.materialise.com/shop/designer/oskarpuzzle, https://www.chewiescustompuzzles.com/puzzleshop/oskars-puzzles