Stellated octahedron

The stellated octahedron is the only <a href="/facts/Stellation/T7NY6CWv">stellation</a> of the <a href="/facts/Octahedron/G38q92xW">octahedron</a>. It is also called the stella octangula (Latin for "eight-pointed star"), a name given to it by <a href="/facts/Johannes_Kepler/wk6GTN3C">Johannes Kepler</a> in 1609, though it was known to earlier <a href="/facts/Geometer/lg9o1Pjo">geometers</a>. It was depicted in <a href="/facts/Pacioli/jaC8rCcG">Pacioli</a>'s <a href="/facts/Divina_proportione/zum7pq7g">De Divina Proportione</a>, 1509.
It is the simplest of five regular <a href="/facts/Polyhedral_compound/L13pItNN">polyhedral compounds</a>, and the only regular polyhedral compound composed of only two polyhedra.
It can be seen as a 3D extension of the <a href="/facts/Hexagram/IF4PEJbL">hexagram</a>: the hexagram is a two-dimensional shape formed from two overlapping equilateral triangles, <a href="/facts/Central_symmetry/UzswAm8N">centrally symmetric</a> to each other, and in the same way the stellated octahedron can be formed from two centrally symmetric overlapping tetrahedra. This can be generalized to any desired amount of higher dimensions; the four-dimensional equivalent construction is the <a href="/facts/Compound_of_two_5-cells/Rh6lwDcc">compound of two 5-cells</a>.

Stellated octahedron open-in-new

Stellated octahedron