  Let P_d be a convex polygon with d vertices. The associated Wachspress
surface W_d is a fundamental object in approximation theory, defined as the
image of the rational map w_d from P^2 to P^{d-1}, determined by the Wachspress
barycentric coordinates for P_d. We show w_d is a regular map on a blowup X_d
of P^2, and if d>4 is given by a very ample divisor on X_d, so has a smooth
image W_d. We determine generators for the ideal of W_d, and prove that in
graded lex order, the initial ideal of I(W_d) is given by a Stanley-Reisner
ideal. As a consequence, we show that the associated surface is arithmetically
Cohen-Macaulay, of Castelnuovo-Mumford regularity two, and determine all the
graded betti numbers of I(W_d).
