The only strictly convex tetratile is a square, 4:1^4.

Tetratiles

Tetratiles can fill the plane along the boundaries of a square grid, with angles 90°. All tetratiles have their vertices and edges along the vertices and edges of square graph paper.

Polyominos are edge-to-edge connections of squares, used in puzzles to fill open or closed domains in the plane.

Tilings of simple tetratiles

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