Many man-made objects have intrinsic symmetries and Manhattan structure. By assuming an orthographic projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and/or Manhattan structure cues, which occur when an input is a single image or multiple images from the same category, e.g., multiple different cars. Specifically, analysis on the single image case implies that Manhattan alone is sufficient to recover the camera projection, and then the 3D structure can be reconstructed uniquely exploiting symmetry. However, Manhattan structure can be difficult to observe from a single image due to occlusion. To this end, we extend to the multiple-image case which can also exploit symmetry but does not require Manhattan axes. We propose a novel rigid structure from motion method, exploiting symmetry and using multiple images from the same category as input. Experimental results on the Pascal3D+ dataset show that our method significantly outperforms baseline methods.