About ten years ago I discovered an interesting way to construct a tetrahedral shape by sliding together four rectangular planes in a certain way. By using halfway cuts in the planes it was possible to slide them together, all at once, to become the enclosed tetrahedron. This way of constructing objects and structures, finite and infinite, has been one of my interests from then on. In this paper I will give an insight into some of the results of my research in this field. Besides halfway cuts I examined some other ways of slide-together structures.