Kagomé antiferromagnet with defects: Satisfaction, frustration, and spin folding in a random spin system

It is shown that site disorder induces noncoplanar states, competing with the thermal selection of coplanar states, in the nearest neighbor, classical Kagom\'e Heisenberg antiferromagnet. For weak disorder, it is ofund that the ground state energy is the sum of energies of separately satisfied triangles of spins. This implies that disorder does not induce conventional spin glass behavior. A transformation is presented, mapping ground state spin configurations onto a folded triangular sheet (a new kind of ``spin origami'') which has conformations similar to those of tethered membranes.