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We present an approach for the planar surface reconstruction of a scene from images with limited overlap. This reconstruction task is challenging since it requires jointly reasoning about single image 3D reconstruction, correspondence between images, and the relative camera pose between images. Past work has proposed optimization-based approaches. We introduce a simpler approach, the PlaneFormer, that uses a transformer applied to 3D-aware plane tokens to perform 3D reasoning. Our experiments show that our approach is substantially more effective than prior work, and that several 3D-specific design decisions are crucial for its success.