| 翻訳と辞書 |
| Socolar-Taylor tile ： ウィキペディア英語版 |
Socolar–Taylor tile
The Socolar–Taylor tile is a single tile which is aperiodic on the Euclidean plane, meaning that it admits only non-periodic tilings of the plane, with rotations and reflections of the tile allowed.〔.〕 It is the first known example of a single aperiodic tile, or "einstein". The basic version of the tile is a simple hexagon, with printed designs to enforce a local matching rule, regarding how the tiles may be placed. This rule cannot be geometrically implemented in two dimensions while keeping the tile a connected set.〔〔
This is, however, possible in three dimensions, and in their original paper Socolar and Taylor suggest a three-dimensional analogue to the monotile.〔 The 3D monotile aperiodically tiles three-dimensional space; however, much as the structure of the 2D tile prevents it from being fitted together just by sliding the tiles together in 2D space, physical copies of the three-dimensional tile could not be fitted together without access to four-dimensional space. This tile is likewise the only known 3D aperiodic tile which can fill three-dimensional space unpredictably.〔
==Gallery==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Socolar–Taylor tile」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|