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WADS
2005
Springer

Hinged Dissection of Polypolyhedra

14 years 6 months ago
Hinged Dissection of Polypolyhedra
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 [DDE+ ] about the special case of polycubes (where P is a cube) and extend analogous results from 2D [DDE+ ], Along the way, we present hinged dissections for polyplatonics (where P is a platonic solid) that are particularly efficient: among a particular type of hinged dissection, they use the fewest possible pieces.
Erik D. Demaine, Martin L. Demaine, Jeffrey F. Lin
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where WADS
Authors Erik D. Demaine, Martin L. Demaine, Jeffrey F. Lindy, Diane L. Souvaine
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