It’s been a year of endless einsteins. In March, a troupe of mathematical tilers announced that they had discovered an “aperiodic monotile,” a shape that can tile an infinite flat surface in a pattern that does not repeat — “einstein” is the geometric term of art for this entity. David Smith, a shape hobbyist in England who made the original discovery and investigated it with three collaborators possessing mathematical and computational expertise, nicknamed it “the hat.” (The hat tiling allows for reflections: the hat-shaped tile and its mirror image.)

Now, the results are in from a contest run by the National Museum of Mathematics in New York and the United Kingdom Mathematics Trust in London, which asked members of the public for their most creative renditions of an einstein. A panel of judges assessed 245 submissions from 32 countries. Three winners were chosen, and, on Tuesday, there will be a ceremony at the House of Commons in London. (Each winner receives an award of 5,000 British pounds; nine finalists receive 1,000 pounds.)

Among the judges was Mr. Smith, who said in an email that he was “captivated by the diversity and high standard of all the entrants.”

What would you do with an einstein tile?

Play it

For the finalist William Fry, 12, of New York, the answer was: Play Tetris, of course! He named his monotile variant of the game Montris. (Another entrant had a similar idea, called Hatris.) His sister, Leslie Fry, 14, received an honorable mention for a collage inspired by Paddington Bear and his famous red hat.

Eat it

Evan Brock, 31, an exhibit designer in Toronto, took one of the three top prizes with his hat ravioli. Prepared with bespoke wood molds, it promises “a more geometric dining experience,” his submission notes.

Stuffed with potato-and-onion filling, Mr. Brock’s ravioli are made from yellow (turmeric), orange (carrot) and red (beet) doughs for unreflected hat tiles; and green (spinach) dough for reflected tiles. Other edible entries included hat cakes and hat cookies, hat sandwiches and hat dosas. “But these ravioli made us laugh,” Chaim Goodman-Strauss, one of Mr. Smith’s collaborators, a judge and an outreach mathematician at the National Museum of Mathematics, said in an email. “They look so tasty, too.”

… (and so on)