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In this paper, we propose an unwrappable representation for image-based façade modeling from multiple registered images. An unwrappable façade is represented by the mutually orthogonal baseline and profile. We first reconstruct semidense 3D points from images, then the baseline and profile are extracted from the point cloud to construct the base shape and compose the textures of the building from the images. Through our unwrapping process, the reconstructed 3D points and composed textures are further mapped to an unwrapped space that is parameterized by the baseline and profile. In doing so, the unwrapped space becomes equivalent to the planar space in which planar façade modeling techniques can be used to reconstruct the details of the buildings. Finally, the augmented details can be wrapped back to the original 3D space to generate the final model. This newly introduced unwrappable representation extends the state-of-the-art modeling for planar façades to a more general class of façades. We demonstrate the power of the unwrappable representation with a few examples in which the façade is not planar.