Hinged Dissection of Polypolyhedra
Hinged Dissection of Polypolyhedra
复制标题
多多面体的铰接解剖
DOI：
10.1007/11534273_19
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
D. Souvaine
中科院分区：
文献类型：
--
作者：
E. Demaine;M. Demaine;Jeffrey F. Lindy;D. Souvaine
本文给出了多面体的一般三维铰接剖分族，通过沿沿着相同面连接同一多面体的几个刚性副本而形成的连接三维实体。(Such只有反射对称的面才有可能连接。每个铰接的剖分由线性数量的固体多面体片组成，这些多面体片沿其边缘沿着铰接以形成柔性闭合链（循环）。对于每个基本多面体P和每个正整数n，单个铰接剖分具有对应于通过连接n个多面体P的副本而形成的所有可能多面体的折叠构型。特别地，这些结果解决了文献[7]中提出的关于多立方体（其中P是立方体）的特殊情况的公开问题，并推广了2D [7]中的类似结果。沿着这条路，我们提出了多柏拉图体（其中P是柏拉图体）的铰链剖分，它们特别有效：在一种铰链剖分中，它们使用尽可能少的块。
This paper presents a general family of 3D hinged dissections forpolypolyhedra, 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 polyhedronPand each positive integern, a single hinged dissection has folded configurations corresponding to all possible polypolyhedra formed by joiningncopies of the polyhedronP. In particular, these results settle the open problem posed in [7] about the special case of polycubes (wherePis a cube) and extend analogous results from 2D [7].Along the way, we present hinged dissections for polyplatonics (wherePis a platonic solid) that are particularly efficient: among a type of hinged dissection, they use the fewest possible pieces.