Let $T$ be a collection of functions from $X$ to $Y$, and call them ``tableaux". I'll describe a simplicial complex whose facets correspond exactly to these tableaux, with many good properties. \vskip .1in \noindent Something particularly nice happens if $X$ is a poset, $Y$ is totally ordered, and the tableaux are weakly order-preserving functions; then the simplicial complex is homeomorphic to a ball. (This is a sign of an interesting complex, and I'll recall why.) \vskip .1in \noindent This work is joint with Ezra Miller and Alex Yong (both in Minnesota).