“…1c), 16 and Shastry–Sutherland lattices; 17 and 3D systems of cube tile lattices, 18 pyrochlore (or breathing pyrochlore) lattices, 19 diamond lattices, 20 hyper-Kagomé lattices, 21 and hyper-honeycomb lattices, 22 have been theoretically proposed. Meanwhile, experimentally, a number of magnetic compounds with their corresponding spin lattices have been realized and investigated, for example, zigzag chains of SrCuO 2 , 23 BaTb 2 O 4 , 24 MIO 3 F (M = Co and Ni), 25 and MnWO 4 ; 26 diamond chains of Cu 3 (CO 3 ) 2 (OH) 2 , 27 K 3 Cu 3 AlO 2 (SO 4 ) 4 , 28 and Cu 2 FePO 4 F 4 (H 2 O) 4 ; 29 spin ladders of ACu 2 O 3 (A = Sr, Ca) 30,31 and Sr 2 Cu 3 O 5 ; 32 triangular lattices of YbMgGaO 4 33,34 and NaYbS 2 ; 35,36 Kagomé lattices of ZnCu 3 (OH) 6 Cl 2 37,38 and Cu 3 V 2 O 7 (OH) 2 ·2H 2 O; 39,40 square lattices of Li 2 VOAO 4 (A = Si, Ge) 41 and VOMoO 4 ; 42 honeycomb lattices of A 2 IrO 3 (A = Na, Li, Cu), 43,44 α-RuCl 3 , 45 and NaIrO 3 ; 46 Shastry–Sutherland lattices of SrCu 2 (BO 3 ) 2 47 and (CuCl)LaNb 2 O 7 ; 48 the cube lattice of CsFe 3 (SeO 3 ) 2 F 6 ; 49 pyrochlore lattices of RE 2 Ti 2 O 7 (RE = Yb, Dy, Ho), 50 Lu 2 Mo 2 O 7 and Lu 2 Mo 2 O 5 N 2 ; 51 the diamond lattice of NiRh 2 O 4 ; 52 the hyper-Kagomé lattice of Na 4 Ir 3 O 8 ; 53 and the hype-honeycomb lattice of β-Li 2 IrO 3 . 54…”