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- Q18204561 subject Q21980955.
- Q18204561 subject Q7132786.
- Q18204561 abstract "The einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles, that is, a shape that can tessellate space, but only in a nonperiodic way. Such a shape is called an "einstein", a play on the German words ein stein, meaning one tile. Depending on the particular definitions of nonperiodicity and the specifications of what sets may qualify as tiles and what types of matching rules are permitted, the problem is either open or solved. The einstein problem can be seen as a natural extension of the second part of Hilbert's eighteenth problem, which asks for a single polyhedron that tiles Euclidean 3-space, but such that no tessellation by this polyhedron is isohedral. Such anisohedral tiles were found by Karl Reinhardt in 1928, but these anisohedral tiles all tile space periodically.".
- Q18204561 thumbnail Socolar-Taylor_tile.svg?width=300.
- Q18204561 wikiPageWikiLink Q101749.
- Q18204561 wikiPageWikiLink Q11059889.
- Q18204561 wikiPageWikiLink Q17002261.
- Q18204561 wikiPageWikiLink Q17078320.
- Q18204561 wikiPageWikiLink Q193657.
- Q18204561 wikiPageWikiLink Q211459.
- Q18204561 wikiPageWikiLink Q214856.
- Q18204561 wikiPageWikiLink Q21980955.
- Q18204561 wikiPageWikiLink Q222032.
- Q18204561 wikiPageWikiLink Q245462.
- Q18204561 wikiPageWikiLink Q268961.
- Q18204561 wikiPageWikiLink Q3847067.
- Q18204561 wikiPageWikiLink Q4765348.
- Q18204561 wikiPageWikiLink Q5450441.
- Q18204561 wikiPageWikiLink Q7132786.
- Q18204561 wikiPageWikiLink Q741518.
- Q18204561 wikiPageWikiLink Q7439094.
- Q18204561 wikiPageWikiLink Q852195.
- Q18204561 comment "The einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles, that is, a shape that can tessellate space, but only in a nonperiodic way. Such a shape is called an "einstein", a play on the German words ein stein, meaning one tile. Depending on the particular definitions of nonperiodicity and the specifications of what sets may qualify as tiles and what types of matching rules are permitted, the problem is either open or solved.".
- Q18204561 label "Einstein problem".
- Q18204561 depiction Socolar-Taylor_tile.svg.