**Reference**:- Erik D. Demaine, Martin L. Demaine, Jin-Ichi Itoh, and Chie Nara, “Continuous flattening of orthogonal polyhedra”, in
*Revised Papers from the 18th Japan Conference on Discrete and Computational Geometry and Graphs (JCDCGG 2015)*, Lecture Notes in Computer Science, volume 9943, Kyoto, Japan, September 14–16, 2015, pages 85–93. **Abstract**:-
Can we flatten the surface of any 3-dimensional polyhedron
*P*without cutting or stretching? Such continuous flat folding motions are known when*P*is convex, but the question remains open for nonconvex polyhedra. In this paper, we give a continuous flat folding motion when the polyhedron*P*is an orthogonal polyhedron, i.e., when every face is orthogonal to a coordinate axis (*x*,*y*, or*z*). More generally, we demonstrate a continuous flat folding motion for any polyhedron whose faces are orthogonal to the*z*axis or the*xy*plane. **Comments**:- This paper is also available from SpringerLink.
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**Related papers**:- FlatteningOrthogonal_JCDCGG2015 (Continuous flattening of orthogonal polyhedra)

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Last updated July 7, 2019 by Martin Demaine.