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In Kato-Nakayama-Usui's theory, a certain space of nilpotent orbits can beconstructed and serve as a completion of a given period map. This can beregarded as a generalization of Mumford's toroidal compactification for locallysymmetric varieties.  Kato-Nakayama-Usui's construction requires the existence of a weak fan, whichis not known in general for non-classical cases. In this paper, we show aftersome slight modifications, such weak fans exist for a large class of periodmaps of weight 3 Calabi-Yau type. In particular, for these cases aKato-Nakayama-Usui type completion can be constructed.

Space of nilpotent orbits and extension of period maps (I): The weight 3 Calabi-Yau types