monotile

plural monotiles

1. geometryA prototile tiling monohedrally; any shape able to completely tile some space on its own (allowing for translation, rotation, and reflection).

   An aperiodic monotile never repeats a formation, no matter how long the pattern.

   2023 April 4, Matthew Cantor, “'The miracle that disrupts order': mathematicians invent new 'einstein' shape”, in The Guardian, London: Guardian News & Media, →ISSN, →OCLC, archived from the original on 04 Apr 2023

   3 more examples

   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.

   1995, Marjorie Senechal, Quasicrystals and Geometry, Cambridge, Cambridgeshire: Cambridge University Press, →ISBN, page 208

   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.

   1997, Rudy Rucker, Freeware (Ware Tetralogy; 3), New York, N.Y.: Avon Books, →ISBN, page 69

   This naturally led to serious rumination about the possible existence of a single tile, or monotile, that forces non-periodic global structure.

   2007 March, Joshua E. S. Socolar, “More ways to tile with only one shape polygon”, in The Mathematical Intelligencer, volume 29, number 2, New York, N.Y.: Springer, →DOI, →ISSN, →OCLC, page 33