A pentomino is a polyomino composed of five congruent squares, connected along their edges (which sometimes is said to be an orthogonal connection).
There are twelve different free pentominoes. Ordinarily, the pentomino obtained by reflection or rotation of a pentomino does not count as a different pentomino.
I discovered pentominoes as a nerdy kid, probably when I read one of Martin Gardner's books based on his "Mathematical Games" columns in "Scientific American". Many of them are still available and I recommend them to anyone who has a mathematical mind (or whose children have).
The logo at the top of each of my pages is one example of a 5x12 tiling of free pentominoes and the the strip at the bottom is repeated copies of a 3x20 tiling.
The logo and strip are derived from the above work by a Wikipedia contributor and are used under a Creative Commons licence. See here for the gory details.