Geometrical frustration is an important feature in magnetism, where it stems from the relative arrangement of spins. A simple 2D example is shown in Figure 1. Three magnetic ions reside on the corners of a triangle with antiferromagnetic interactions between them; the energy is minimized when each spin is aligned opposite to neighbors. Once the first two spins align antiparallel, the third one is frustrated because its two possible orientations, up and down, give the same energy. The third spin cannot simultaneously minimize its interactions with both of the other two. Since this effect occurs for each spin, the ground state is sixfold degenerate. Only the two states where all spins are up or down have more energy.