Imagine two triangles in the three-dimensional space， such that an edge of the one pierces through the interior of the other， and vice versa. In such a geometrical situation， any continuous transformation that separates the two triangles would lead to an intersection of their boundaries at one moment， and so we call the two triangles and their boundaries linked （germ： "verschlungene Dreiecke"）.
　　It is a known fact in graph theory [8] that any embedding of the complete graph with 6 vertices K6 into R3 has at least one pair of those linked triangles. Prof.Dr.U.Brehm （TU-Dresden）， who was my advisor during this diploma thesis， used the so called Gale diagrams to proof that any straight line embedding of the K6 contains either one or exactly three pairs of linked triangles. In Section 1.3.1 we will explain this technique， which leads to the proof of the corresponding Theorem 1.4， and we give visual examples for both cases in Figure 2.