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‘The hat’: 50-year-old geometry mystery

Facts for Prelims (FFP)

Source: TH


Context: A group of scientists have discovered a new shape with 13 sides, named ‘the hat’, It is the first ‘einstein’ tile (‘ no relation to Albert Einstein’ ) to have been found: a shape that can cover a plane without overlapping, leaving gaps, or repeating patterns.



Shape: polykite with the edges of eight kites to make it



Fig: The grey area shows the polykite shape of ‘the hat’



The discovery has answered a long-standing question in the field of plane geometry and generated excitement in the scientific community. It is the first time a single aperiodic tile has been found to cover a plane, which has been long-awaited as the number of shapes in a tile has decreased over the years.