In this thesis, we will give a way to build mechanical metamaterials. We will do this by using a triangular tiling, in which we put spins on the edges of the tiles. These spins have to point either...Show moreIn this thesis, we will give a way to build mechanical metamaterials. We will do this by using a triangular tiling, in which we put spins on the edges of the tiles. These spins have to point either into or out of the triangles and have to satisfy the rule that for every triangle two spins have to point out, and one in, or two spins point in and one out. If we can construct a tiling that is completely filled with these triangles in such a way that all spins on sides of adjacent triangles are pointing in the same direction, we will call this a feasible configuration. Firstly, we derive the number of feasible configurations for the tiling and consider a way to estimate these values. Secondly, we derive the distribution for the number of configurations when there are i spins on the boundary pointing in. Finally, we consider the number of spins in a periodic tiling that can be reversed, independent of all other spins, and derive an upper value and a lower boundary for this.Show less
