在這篇論文中，我們主要想找出一個有效的方法來解開在三維空間中的環面簇的奇異點。我們知道，解開環面簇的奇異點可以透過一些加邊的動作。但事實上，所需要插入的邊是有一定的次序，而且有時可能需要插入很多的邊才能完全解開環面簇的奇異點。因此，找出一個最有效、最精簡的方法就變得非常重要。在二維的空間中，確實可以透過連分數的關係找出一個最精簡的分割方法。在三維空間中，我們仿照二維可以找到一個有效的分割方法。進一步地，我們提供了一個程式讓大家很明確的知道所要加的邊和分割的方法(參考附錄1、2)。但在三維空間中，因為所要討論的可能性和變數變多了，所以我們不確定這是不是最精簡的。不過，這已經是我們所能找出的方法中最有效的。

In this paper, we will introduce an effective method to find primitive vectors we insert in a three-dimensional
nonsmooth simplicial cone σ such that σ is smoothly subdivided and a precise way to subdivided σ into
three-dimensional smooth simplicial cones. Further, we design a computer program to help us to operate all necessary added
primitive vectors by using our method. But we can not say that the method we use is a minimal solution. For the future, we will
keep to resolve this problem.

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