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Human facial expressions change dynamically, so their recognition / analysis should be conducted by accounting for the temporal evolution of face deformations either in 2D or 3D. While abundant 2D video data do exist, this is not the case in 3D, where few 3D dynamic (4D) datasets were released for public use. The negative consequence of this scarcity of data is amplified by current deep learning based-methods for facial expression analysis that require large quantities of variegate samples to be effectively trained. With the aim of smoothing such limitations, in this paper we propose a large dataset, named Florence 4D, composed of dynamic sequences of 3D face models, where a combination of synthetic and real identities exhibit an unprecedented variety of 4D facial expressions, with variations that include the classical neutral-apex transition, but generalize to expression-to-expression. All these characteristics are not exposed by any of the existing 4D datasets and they cannot even be obtained by combining more than one dataset. We strongly believe that making such a data corpora publicly available to the community will allow designing and experimenting new applications that were not possible to investigate till now. To show at some extent the difficulty of our data in terms of different identities and varying expressions, we also report a baseline experimentation on the proposed dataset that can be used as baseline.