Starminx refers to two dodecahedral puzzles designed and manufactured by mf8. Both have faces in the form of inscribed pentagrams, hence the name.
The "Starmminx 1", which confusingly was actually the second, is a vertex-cut puzzle. It works in a similar fashion to the Dino Cube (twisting a corner moves three edges around, although in this case they also have a triangular centre piece between them). This, plus the fact that the pentagonal face centres never move, gives this one a similar low level of difficulty to that of the Dino Cube. This puzzle is probably also similar to (although not isomorphic with) the Alexander's Star.