Polyominos are tiles created as the union of edge-to-edge connected square. They are classified by the number of squares monomino=1, domino=2, tromino=3, tetromino=4, pentomino=5, hexomino=6, heptomino=7, octomino=8, nonomino=9, decomino=10. They can be enumerated with different counts, allowing or disallowing rotations, allowing or disallowing reflections, and allowing or disallowing holes.
There's only one monomino, a square, and one domino, a 2x1 rectangle with 2 orientations. There are 2 triminos, with 6 orientations. There are 5 tetrominos, with 19 orientations. Two of the 5 are chiral, having pairs of mirror image forms. The game Tetris has falling Tetrominos which have to fill a solid level to clear.
Polyominos can make puzzles, how to fill (dissect) a given permeter of squares with a given set of polyominos.
Tetratile notation can express all of them in either equilateral or equiangular notation. Equilateral notation starts with 4: and sequences angles -1,0,1. Equiangular notation starts with <4>: and sequences integer edge lengths, with a negative sign for cw turns.