A set of new canonical variables for d = 11 supergravity is proposed which renders the supersymmetry variations and the supersymmetry constraint polynomial. The construction is based on the SO(1, 2) × SO(16) invariant reformulation of d = 11 supergravity given in [4], and has some similarities with Ashtekar's reformulation of Einstein's theory. The new bosonic variables fuse the gravitational degrees of freedom with those of the three-index photon AMNP in accordance with the hidden symmetries of the dimensionally reduced theory. Although E8 is not a symmetry of the theory, the bosonic sector exhibits a remarkable E8 structure, hinting at the existence of a novel type of "exceptional geometry".Recent advances in string theory (see e.g. [1]) have lent renewed support to the long held belief that d = 11 supergravity [2] has a fundamental role to play in the unification of fundamental interactions. In this letter, we present an unconventional formulation of this theory, developing further the results of refs. [3,4] where new versions of d = 11 supergravity with local SO(1, 3) × SU(8) and SO(1, 2) × SO(16) tangent space symmetries, respectively, were presented. In both versions the supersymmetry variations were shown to acquire a polynomial form from which the corresponding formulas for the maximal supergravities in four and three dimensions can be read off directly and without the need for complicated duality redefinitions.