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English
A tiling using rhombic dodecahedron monotilesA tiling using aperiodic "hat" monotiles
In the following section we will describe families of tilings by a curious three-dimensional aperiodic monotile whose matching rule — for some values of its parameter — is weak but not strong.
And I am sorry I never delivered on the four-dimensional Poultry design. It turns out John Horton Conway found four-dimensional and five-dimensional aperiodic monotiles sixty years ago, but it's not too well documented.
Siobhan Roberts (2023 March 28) “Elusive 'Einstein' Solves a Longstanding Math Problem”, in The New York Times, New York, N.Y.: The New York Times Company, →ISSN, →OCLC, archived from the original on 2023-04-04: “Dr. Goodman-Strauss had raised this subtlety on a tiling listserv: "Is there one hat or two?" The consensus was that a monotile counts as such even using its reflection.”
Einstein problem on Wikipedia.Wikipedia 