An Algorithm for Folding a Conway Tile into an Isotetrahedron or a Rectangle Dihedron
An Algorithm for Folding a Conway Tile into an Isotetrahedron or a Rectangle Dihedron
复制标题
将康威瓷砖折叠成等四面体或矩形二面体的算法
DOI：
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发表时间：
2020
影响因子：
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通讯作者：
Kiyoko Matsunaga
中科院分区：
文献类型：
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作者：
J. Akiyama;Kiyoko Matsunaga
等四面体(I)或矩形二面体(RD)的每一个网都是Conway瓦片。反之，利用Alexandrov定理证明了每一个Conway瓷砖都可以折叠成I或RD。然而，当时还不知道如何将给定的康威瓷砖折叠成I或RD。本文的目的是给出一种将Conway瓷砖折叠成I或RD的算法。此外，对于给定的Conway瓷砖，我们提出了一种方法来识别它可以折叠成的I或RD的确切形状。
: Every net of an isotetrahedron (I) or a rectangle dihedron (RD) is a Conway tile. Reversely, it is shown by using Alexandrov’s theorem that every Conway tile can be folded into either I or RD. However, it was not known how to fold a given Conway tile into I or RD. The purpose of this paper is to give an algorithm for folding a Conway tile into I or RD. Moreover, for a given Conway tile we present a method to identify the exact shape of I or RD into which it can be folded.