monotile

English

A tiling using rhombic dodecahedron monotiles

A tiling using aperiodic "hat" monotiles

Etymology

From mono- (“one”) +‎ tile.

Noun

monotile (plural monotiles)

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

   Hyponym: einstein

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

     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.

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

     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.

     The story takes place in 2053.

   • 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:

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

   • 2023 April 4, Matthew Cantor, “'The miracle that disrupts order': mathematicians invent new 'einstein' shape”, in The Guardian‎^[1], London: Guardian News & Media, →ISSN, →OCLC, archived from the original on 2023-04-04:

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

Related terms

• monotiling

 

References

• Siobhan Roberts (2023 March 28) “Elusive 'Einstein' Solves a Longstanding Math Problem”, in The New York Times‎^[2], 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.”

Further reading

• Einstein problem on Wikipedia.Wikipedia