本論文主要是探討鑲嵌於單階晶格的多邊形之展開演算法，
且在展開演算法中，不允許任何不相連的邊有交叉。
我們先證明了所有鑲嵌於深度為n的兩列單階晶格的未打結多邊形一定可以在O(n^2)的時間內展開，
然後也證明了鑲嵌於3x3單階晶格的未打結多邊形也一定可以折到兩列單階晶格內。
我們的演算法中最核心的部份是我們需要把所有多邊形的區塊由右往左的全部折起來，
使原本三維的多邊形被折成一個二維的凸多邊形。
我們最後提出了一個未解的問題:「是否所有鑲嵌於晶格的未打結多邊形都是可展開的?」，且希望這篇論文可以使我們離解開這個問題更靠近一步。

We consider the problems of unfolding lattice polygons lying in a width-2 lattice of unit height.
During the unfolding process, all linkage edges are preserve and no edge crossing are allowed.
Let n be the depth of edges of the given lattice polygon.
We first show that a unknotted lattice polygon lying in a 3D width-2 lattice of unit height can be unfolded in O(n^2) moves and time.
We then show that a unknotted lattice polygon lying in a 3D 3x3 lattice of unit height can be reconfigured to a 2x2 lattice polygon.
The main technique in our algorithms is to fold up all blocks of the lattice polygon from the rightmost cubic cells of the given lattice.
We hope that our results shed some light on solving the more general conjectures, which we proposed, that a 3D unknotted lattice polygon lying in any lattice can always be unfolded.

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