I'm trying to get an intuitive feel for product spaces, and I think I am having some trouble. I understand that the product space S1 x S1 is a torus. the two circles are cycles which are not boundaries though. What happens when you take the product space of two cycles which are boundaries? For example, the product space of two 2-simplices. Is there any "intuitive" way to understand what will happen when you multiply two simplices?