The stellated octahedron, or stella octangula, is the only stellation of the octahedron. It was named by Johannes Kepler in 1609, though it was known to earlier geometers. It was depicted in Pacioli's Divina Proportione, 1509.
It is the simplest of five regular polyhedral compounds.
It can be seen as a 3D extension of the Star of David (as it is two tetrahedra overlapping each other), and as a stage in the construction of a 3D Koch Snowflake (as it is four small tetrahedra attached to a central, larger one).