  We study the moduli spaces of polygons in R^2 and R^3, identifying them with
subquotients of 2-Grassmannians using a symplectic version of the
Gel'fand-MacPherson correspondence. We show that the bending flows defined by
Kapovich-Millson arise as a reduction of the Gel'fand-Cetlin system on the
Grassmannian, and with these determine the pentagon and hexagon spaces up to
equivariant symplectomorphism. Other than invocation of Delzant's theorem, our
proofs are purely polygon-theoretic in nature.
