The word stellation comes from the Latin word stella, meaning star. A polyhedron is stellated by extending the planes that contain the faces of the polyhedron beyond the edges of the polyhedron until they intersect at a new set of edges, forming a star. Often if the planes are extended farther, they will intersect again, and several stars can be formed.

This can be demonstrated in two dimensions.

This is a regular octagon.

By extending the sides, a star can be formed. This is the first stellation. This figure is also called a 2-square compound, since it can be formed from 2 squares.

By extending the sides farther, another star can be formed. This is the second stellation.