Tetromino

A tetromino is a geometric shape composed of four squares, connected orthogonally (i.e. at the edges and not the corners).

The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected orthogonally.

That is, two free polyominos are the same if there is a combination of translations, rotations, and reflections that turns one into the other.

By extension, any odd number of sets for either type cannot fit in a rectangle.

The name was introduced by Solomon W. Golomb in 1953 along with other nomenclature related to polyominos.

J and L are the same tetracube, as are S and Z, because one may be rotated around an axis parallel to the tetromino's plane to form the other.

Three more tetracubes are possible, all created by placing a unit cube on the bent tricube: The tetracubes can be packed into two-layer 3D boxes in several different ways, based on the dimensions of the box and criteria for inclusion.