The wedge product is said to be associative (e.g. http://mathworld.wolfram.com/WedgeProduct.html ). The cross product is not associative. But the Hodge star is said to give an isomorphism between 3-dimensional (mono?)vectors and their bivectors. How is this possible when "if two objects are isomorphic, then any property which is preserved by an isomorphism and which is true of one of the objects, is also true of the other" ( http://en.wikipedia.org/wiki/Isomorphism ). Is the isomorphism given by the Hodge star with respect to vector addition only, and not also the cross and wedge products? A component expression for the wedge product can be computed by a determinant in the same way as that of the cross product, suggesting that the wedge should be just as non-associative as the cross product. How is this apparent contradiction resolved: am I misunderstanding something about the cross product, the wedge product, the Hodge star, associativity or isomorphism or...?