Piezoelectricity and Piezomagnetism : Duality in Two-Dimensional Checkerboards

The duality approach in 2-{\it dim} two-component regular checkerboards was extended onto piezoelectricity and piezomagnetism problems. There are found a relation for effective piezoelectric and piezomagnetic modules for the checkerboard with $p6^{\prime} mm^{\prime}$-plane symmetry group ({\em dichromatic triangle}). \pacs{Pacs: 73.50.Bk,Jt, 75.70.Ak, 77.65.-j, 77.84.Lf}