\'Einstein tile\' or \'the hat\' was in news recently, it is used in terms of:

Question

Several ways of tiling exists in nature and the real world like bathroom tiles or the hexagons of honeycomb. All of these are periodic and have a translation symmetry, i.e., the size, shape and angle remains the same, only the location changes.
The 13-sided ‘hat’ discovered is also a shape that tiles plane, however, it does not possess translational symmetry. These types of shapes are called aperiodic tile sets.
It is the first ‘Einstein’ tile to have been found. The ‘Einstein’ tile is an aperiodic monotile.
‘Einstein’ tile is a shape that can cover a plane without overlapping, leaving gaps, or repeating patterns. The tile has no connection with Albert Einstein.

GKToday Admin · Accepted Answer

Thirteen sided aperiodic monotile

Several ways of tiling exists in nature and the real world like bathroom tiles or the hexagons of honeycomb. All of these are periodic and have a translation symmetry, i.e., the size, shape and angle remains the same, only the location changes.
The 13-sided ‘hat’ discovered is also a shape that tiles plane, however, it does not possess translational symmetry. These types of shapes are called aperiodic tile sets.
It is the first ‘Einstein’ tile to have been found. The ‘Einstein’ tile is an aperiodic monotile.
‘Einstein’ tile is a shape that can cover a plane without overlapping, leaving gaps, or repeating patterns. The tile has no connection with Albert Einstein.

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