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Questions about Tessellation

Short answers, pulled from the story.

When did the Sumerians create the earliest known tessellation patterns in Uruk IV?

The Sumerian city of Uruk IV created a temple mosaic with tessellation patterns between 3400 and 3100 BC. This artifact marks one of humanity's earliest uses of geometric covering using colored tiles.

Who proved that every periodic tiling of the plane features one of seventeen different groups of isometries?

Russian crystallographer Yevgraf Fyodorov made this proof in 1891. His work marked the unofficial beginning of the mathematical study of tessellations.

What shapes can form regular tessellations without gaps or overlaps?

Only three shapes can form such regular tessellations: equilateral triangles, squares, and regular hexagons. These identical regular polygonal tiles all share the same shape to cover a surface completely.

Which tile was discovered in March 2023 as the first einstein tile for aperiodic tiling?

David Smith discovered the hat tile in March 2023 alongside Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. Their paper appeared as arXiv:2303.10798 on the 2nd of May 1536.

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