**Reference**:- Erik D. Demaine, Martin L. Demaine, Jeffrey F. Lindy, and Diane L. Souvaine, “Hinged Dissection of Polypolyhedra”, in
*Proceedings of the 9th Workshop on Algorithms and Data Structures (WADS 2005)*, Lecture Notes in Computer Science, volume 3608, Waterloo, Ontario, Canada, August 15–17, 2005, pages 205–217. **Abstract**:-
This paper presents a general family of 3D hinged dissections
for
*polypolyhedra*, i.e., connected 3D solids formed by joining several rigid copies of the same polyhedron along identical faces. (Such joinings are possible only for reflectionally symmetric faces.) Each hinged dissection consists of a linear number of solid polyhedral pieces hinged along their edges to form a flexible closed chain (cycle). For each base polyhedron*P*and each positive integer*n*, a single hinged dissection has folded configurations corresponding to all possible polypolyhedra formed by joining*n*copies of the polyhedron*P*. In particular, these results settle the open problem posed in [9] about the special case of polycubes (where*P*is a cube) and extend analogous results from 2D [9]. Along the way, we present hinged dissections for polyplatonics (where*P*is a platonic solid) that are particularly efficient: among a type of hinged dissection, they use the fewest possible pieces. **Comments**:- This paper is also available from SpringerLink.
**Copyright**:- The paper is \copyright Springer-Verlag.
**Availability**:- The paper is available in PostScript (405k), gzipped PostScript (152k), and PDF (189k).
- See information on file formats.
- [Google Scholar search]
**Related papers**:- HingedPolyforms3D_CGW2004 (Hinged Dissection of Polypolyhedra)
- HingedPolyforms (Hinged Dissection of Polyominoes and Polyforms)

See also other papers by Erik Demaine.

Last updated September 20, 2023 by Erik Demaine.