The Alexander's Star is a vintage twisty puzzle. It dates way back to the early eighties. It was invented by an American mathematician called Adam Alexander. It has 30 moving pieces which you move in groups of 5 around each of the 12 vertices.
Although this is quite an impressive puzzle to look at, it's an absolute pain to twist. It is (in)famous for being stiff and fragile. There don't seem to be any new versions available - you have to look on ebay for second-hand ones. Like all rare puzzles, they can go for quite a price. Getting hold of one at a decent price requires some patience and being prepared to lose the auction if the price goes to far.
All this makes the star a bit of a collector's item but by no means an essential item. As you can see in the image, my star remains unsolved - one of the few puzzles that I don't store in its solved state because of its awkwardness.