Techniques are described herein for generating and using a unified shape representation that encompasses features of different types of shape representations. In some embodiments, the unified shape representation is a unicode comprising a vector of embeddings and values for the embeddings. The embedding values are inferred, using a neural network that has been trained on different types of shape representations, based on a first representation of a three-dimensional (3D) shape. The first representation is received as input to the trained neural network and corresponds to a first type of shape representation. At least one embedding has a value dependent on a feature provided by a second type of shape representation and not provided by the first type of shape representation. The value of the at least one embedding is inferred based upon the first representation and in the absence of the second type of shape representation for the 3D shape.