Herein, we automatically learn a latent representation of the cavities of porous cages from a training dataset of 74 porous organic cage molecules. We achieve this by first computationally scanning the cage molecules to generate 3D images of their porosity, with the cavity in the center of the image. The pixels in the image represent a point in space and the binary pixel values represent whether the space is void or occupied by a cage atom. We postulate that these 3D porosity images, which belong to an enormous space, approximately lay in a much lower-dimensional subspace. Inspired by eigenfaces in facial recognition, we then employ the singular value decomposition to, in an unsupervised manner, identify a set of characteristic 3D porosity images-eigencages-that form an orthonormal basis for this approximate, lower-dimensional subspace in which the 3D porosity images lay. A lowdimensional latent representation follows by expressing each cage as a combination of the eigencages. Visualizing a 2D embedding of our latent cage space with t-SNE shows that the learned encoding captures salient features of the cavities of porous cages and is predictive of simulated xenon/krypton selectivity in isolated cage molecules.