We show that several classes of polyhedra are joined by a sequence of O(1)refolding steps . Each refolding step unfolds the current polyhedron and folds thatunfolding into exactly the next . Polyhedron is refoldable into another if they share a common unfolding . In particular, we obtain at most 6-step refolding sequence between any pair of Platonic solids, applying (5) for the dodecahedron . As far as the authors know, this is the first resultabout common unfolding involving the regular dodechedron, as far as well as the . authors know of the result about common unfolding in the regular . dodechesron. This is the . first result about the dodechehedron. As far

Author(s) : Erik D. Demaine, Martin L. Demaine, Yevhenii Diomidov, Tonan Kamata, Ryuhei Uehara, Hanyu Alice Zhang

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Keywords : unfolding - common - refolding - regular - polyhedron -

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