It is also called the stella octangula (Latin for "eight-pointed star"), a name given to it by Johannes Kepler in 1609, though it was known to earlier geometers.

It can also be seen as one of the stages in the construction of a 3D Koch snowflake, a fractal shape formed by repeated attachment of smaller tetrahedra to each triangular face of a larger figure.

[5] The obelisk in the center of the Plaza de Europa [es] in Zaragoza, Spain, is surrounded by twelve stellated octahedral lampposts, shaped to form a three-dimensional version of the Flag of Europe.

[6] Some modern mystics have associated this shape with the "merkaba",[7] which according to them is a "counter-rotating energy field" named from an ancient Egyptian word.

[10] The musical project "Miracle Musical" (often stylized as ミラクルミュージカル[11]), spearheaded by Tally Hall member Joe Hawley, uses the stellated octahedron in the artwork and lyrics of their only album, “Hawaii: Part II”, referring to it as the stella octangula.