We undertake an investigation into the spatial structure of the M31 satellite system utilizing the distance distributions presented in a previous publication. These distances make use of the unique combination of depth and spatial coverage of the Pan-Andromeda Archaeological Survey to provide a large, homogeneous sample consisting of 27 of M31s satellites, as well as M31 itself. We find that the satellite distribution, when viewed as a whole, is no more planar than one would expect from a random distribution of equal size. A disk consisting of 15 of the satellites is however found to be highly significant, and strikingly thin, with an rms thickness of just 12.34+0.75 -0.43 kpc. This disk is oriented approximately edge-on with respect to the Milky Way and almost perpendicular to the Milky Way disk. It is also roughly orthogonal to the disk-like structure regularly reported for the Milky Way satellite system and in close alignment with M31's Giant Stellar Stream. A similar analysis of the asymmetry of the M31 satellite distribution finds that it is also significantly larger than one would expect from a random distribution. In particular, it is remarkable that 20 of the 27 satellites most likely lie on the Milky Way side of the galaxy, with the asymmetry being most pronounced within the satellite subset forming the aforementioned disk. This lopsidedness is all the more intriguing in light of the apparent orthogonality observed between the satellite disk structures of the Milky Way and M31.