中文摘要：

三维流形的分类问题一直是拓扑学的热点研究问题，目前为止已有许多较为有效的方法，如Heegaard分解，应用Dehn手术等，但离问题的最终解决还有相当距离．本文对三维空间的四面体经过两两面叠合后形成的所有可能的三维复合形进行了深入研究，包括判断其是否是流形及其在流形状态下基本群的计算．

英文摘要：

The problem about classification of 3-manifold is a very hot problem all the time recently. We have obtained several effective means such as Heegaard decomposition, Dehn surgery etc. But these are all far from to the final solution. In this paper, we study deeply all possible 3-dimentional complex made up tetrahedron by superimpose a surface to an otherone. Our research include the judgement that if it is a manifold and the computation of the fundermental group when it is so.