Wachspress Varieties Eugene Wachspress introduced rational barycentric coordinates for convex polygons in R^2, which Warren generalized to all convex polytopes in R^d. These Wachspress barycentric coordinates are the unique rational barycentric coordinates of minimal degree. The Wachspress coordinates of a polytope P in R^d define a map of projective d-space to a projective space spanned by the vertices of P whose image is a Wachspress variety. In this talk, I will describe the Wachspress variety and its defining ideal, which is the ideal of algebraic relations among the Wachspress coordinates. This is joint work with Corey Irving, Hal Schenck, and Greg Smith.