We report quantum oscillations in the underdoped high-temperature superconductor YBa 2 Cu 3 O 6+x over a wide range in magnetic field 28Յ 0 H Յ 85 T corresponding to Ϸ12 oscillations, enabling the Fermi surface topology to be mapped to high resolution. As earlier reported by Sebastian et al. ͓Nature ͑London͒ 454, 200 ͑2008͔͒, we find a Fermi surface comprising multiple pockets, as revealed by the additional distinct quantum oscillation frequencies and harmonics reported in this work. We find the originally reported broad lowfrequency Fourier peak at Ϸ535 T to be clearly resolved into three separate peaks at Ϸ460, Ϸ532, and Ϸ602 T, in reasonable agreement with the reported frequencies of Audouard et al. ͓Phys. Rev. Lett. 103, 157003 ͑2009͔͒. However, our increased resolution and angle-resolved measurements identify these frequencies to originate from two similarly sized pockets with greatly contrasting degrees of interlayer corrugation. The spectrally dominant frequency originates from a pocket ͑denoted ␣͒ that is almost ideally two-dimensional in form ͑exhibiting negligible interlayer corrugation͒. In contrast, the newly resolved weaker adjacent spectral features originate from a deeply corrugated pocket ͑denoted ␥͒. On comparison with band structure, the d-wave symmetry of the interlayer dispersion locates the minimally corrugated ␣ pocket at the "nodal" point k nodal = ͑ / 2, / 2͒, and the significantly corrugated ␥ pocket at the "antinodal" point k antinodal = ͑ ,0͒ within the Brillouin zone. The differently corrugated pockets at different locations indicate creation by translational symmetry breaking-a spin-density wave has been suggested from the suppression of Zeeman splitting for the spectrally dominant pocket. In a broken-translational symmetry scenario, symmetry points to the nodal ͑␣͒ pocket corresponding to holes, with the weaker antinodal ͑␥͒ pocket corresponding to electrons-likely responsible for the negative Hall coefficient reported by LeBoeuf et al. ͓Nature ͑London͒ 450, 533 ͑2007͔͒. Given the similarity in ␣ and ␥ pocket volumes, their opposite carrier type and the previous report of a diverging effective mass in Sebastian et al. ͓Proc. Nat. Am. Soc. 107, 6175 ͑2010͔͒, we discuss the possibility of a secondary Fermi surface instability at low dopings of the excitonic insulator type, associated with the metal-insulator quantum critical point. Its potential involvement in the enhancement of superconducting transition temperatures is also discussed.