Assume i got a lot of triangles where all are equilateral and of the same size. Everytime i would like to stick one edge of a triangle to another edge of triangle. My question is: Is it possible to stick triangle edge to edge such that it forms a ring like structure. What a ring like structure is mean that the we can get the same position of the first triangle after many sticking processes.
What i have thought is that each time we stick a trangle, the position of the new triangle is just the previous triangle times a matrice. But i don't know how to show it is possible or not possible to form a ring. I guess the ans should be no, but is there any proof to this case?