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Whenever the elastic energy of a solid depends on magnetic field, there is a magnetostrictive response. Field-linear magnetostriction implies piezo- magnetism and vice versa. Here, we show that Mn3Sn, a non-collinear anti- ferromanget with Weyl nodes, hosts a large and almost perfectly linear magnetostriction even at room temperature. The longitudinal and transverse magnetostriction, with opposite signs and similar amplitude are restricted to the kagome planes and the out-of-plane response is negligibly small. By studying four different samples with different Mn:Sn ratios, we find a clear correlation between the linear magnetostriction, the spontaneous magneti- zation and the concentration of Sn vacancies. The recently reported piezo- magnetic data fits in our picture. We show that linear magnetostriction and piezomagnetism are both driven by the field-induced in-plane twist of spins. A quantitative account of the experimental data requires the distortion of the spin texture by Sn vacancies. We find that the field-induced domain nucleation within the hysteresis loop corresponds to a phase transition. Within the hys- teresis loop, a concomitant mesoscopic modulation of local strain and spin twist angles, leading to twisto-magnetic stripes, arises as a result of the com- petition between elastic and magnetic energies.