Abstract: We present a co-abstraction method that takes as input a collection of 3D objects, and produces a mutually consistent and individually identity-preserving abstraction of each object. In general, an abstraction is a simpler version of a shape that preserves its main characteristics. We hypothesize, however, that there is no single abstraction of an object. Instead, there is a variety of possible abstractions, and an admissible one can only be chosen conjointly with other objects' abstractions. To this end, we introduce a new approach that hierarchically generates a spectrum of abstractions for each model in a shape collection. Given the spectra, we compute the appropriate abstraction level for each model such that shape simplification and inter-set consistency are collectively maximized, while individual shape identities are preserved.