Some Irreptiles of Order Greater than 20

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A rep-tile is a shape that can be tiled with smaller equally sized copies of the shape. If the tiling uses

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copies, the shape is said to be rep-

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.

An irregular rep-tile (or irreptile) is a shape that can be tiled with copies of itself, not all of the same size. If the tiling uses

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copies, the shape is said to be irrep-

n

. If no two tiles have the same size, the tiling is called perfect. A shape that only allows irregular self-tilings is called a puritile.