The only stellations of Platonic solids which are uniform polyhedra are the three dodecahedron stellations and the great icosahedron.
Platonic Solid Stellations
See also
Dodecahedron Stellations, Icosahedron Stellations, Stella OctangulaExplore with Wolfram|Alpha
References
Webb, R. "Enumeration of Stellations." http://www.software3d.com/Enumerate.php.Referenced on Wolfram|Alpha
Platonic Solid StellationsCite this as:
Weisstein, Eric W. "Platonic Solid Stellations." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlatonicSolidStellations.html