Using either the fully supported or Miller's rules criterion (Webb), the octahedron has two reflexible stellations: the octahedron itself and the stella octangula.
Octahedron Stellation
See also
Octahedron, Stella Octangula, StellationExplore with Wolfram|Alpha
References
Webb, R. "Enumeration of Stellations." http://www.software3d.com/Enumerate.php.Webb, R. "Octahedron." http://www.software3d.com/Octahedron.php.Referenced on Wolfram|Alpha
Octahedron StellationCite this as:
Weisstein, Eric W. "Octahedron Stellation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OctahedronStellation.html