This paper presents a global localization technique for a robot with only linear and angular odometers. The robot, whose configuration is composed of its position and orientation, moves in a fully-known environment by alternating rotations and forward translations. We pose the problem as a discrete-time planning problem in the robot's information space, which encapsulates the uncertainty in the robot's configuration. Our contribution is to show that in any simply-connected, bounded polygonal environment, localization by odometry alone is possible, but only up to the symmetries in the environment