What is the terminology for a subset of a product of sets that is the product of its cross-sections?

Question

Let $X$ and $Y$ be non-empty sets. For every $x \in X$, let $S_x$ be a non-empty subset of $Y$. Define $S := \prod_{x \in X}S_x$. $S$ is a subset of $Y^X$. I think I once saw a name given to this kind of subset, namely one that is the product of its cross sections. Perhaps a pipe, or a tube, or a cylinder, or a cube, or a rectangle, or a prism. I can't recall. Is there a commonly accepted terminology for this kind of subset?