The CLARK Tile: An Aperiodic Monotile in Five Dimensions
We give an explicit compact tile, called CLARK (Chair with Local Asymmetric Registration Keys), in five-dimensional Euclidean space. It modifies a chair of 31 unit five-cubes with 256 rational pyramidal keys. Copies may be translated, rotated or reflected. The selected theorem proves tiling existence, no nonzero translation period in any physical tiling, and a finite full Euclidean symmetry group of cardinality at most 3840 for every such tiling. No registration, matching-rule or hierarchy assumption is imposed. A trivial symmetry group is not asserted.
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