This paper discussed degeneracy and robustness issues in geometric computing by an example of two 3D triangle pairs intersecting ,especially the classification of their various relations. The first key to a problem is to describe this problem. Hence, the complete representation of degeneracies is an important foundation and support to design, improve as well as test a robust geometric computing algorithm. For the first time, this paper studies degeneracies for various triangle pairs in 3D space. Based on projecting reduction, their relationships are classified and a complete sample model is deduced to cover all kinds of degeneracies. The basic strategy is to establish a computed coordinate system. Then by projection, 3D relations are reduced to planar ones. Fixing one triangle, and changing the relative position and size of the other, various relations are classified in the clue of departed, contacted, intersected and overlapped. Consequently, all degeneracies can be got. The method proposed in this paper provides a new way to robustness 3D geometric computing algorithms not only for testing samples but also for algorithm reforming.%通过对两空间三角形关系的分类，讨论了几何退化对几何计算的稳健性的影响力。解决一个问题的第一步是描述这个问题，空间几何退化的完整表述是稳健几何计算算法的设计、改进以及测试的重要基础和保障。首次对空间三角形对的退化进行了深入的研究、全面的梳理。基于投影降维原理，抽取繁杂的空间两三角形关系的规律，分离出完整的空间三角形对的退化样本模型。基本策略是建立计算坐标系，通过投影降维，将空间三角形对的位置关系变成一个固定，只有一个变化的平面位置关系。以相离、接触、相交、内含的线索改变另一三角形的位置和大小，分类出空间三角形对的位置关系，检索出两者的所有退化状态。该方法可以推广到其他三维几何间的退化状态分类和几何计算算法的稳健性设计中。
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