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Rep-tile
In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape. The term was coined as a pun on animal reptiles by the American mathematician Solomon W. Golomb, who used it to describe self-replicating tilings. In 2012 a generalization of rep-tiles called self-tiling tile sets was introduced by Lee Sallows in ''Mathematics Magazine''.
==Terminology==
A rep-tile is labelled rep-''n'' if the dissection uses ''n'' copies. Such a shape necessarily forms the prototile for a tiling of the plane, in many cases an aperiodic tiling.
A rep-tile dissection using different sizes of the original shape is called an irregular rep-tile or irreptile. If the dissection uses ''n'' copies, the shape is said to be irrep-''n''. If all these sub-tiles are of different sizes then the tiling is additionally described as perfect. A shape that is rep-''n'' or irrep-''n'' is trivially also irrep-(''kn'' − ''k'' + ''n'') for any ''k'' > 1, by replacing the smallest tile in the rep-''n'' dissection by ''n'' even smaller tiles. The order of a shape, whether using rep-tiles or irrep-tiles is the smallest possible number of tiles which will suffice.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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