Mn1.4PtSn is the first material in which antiskyrmions have been observed in ultrathin single-crystalline specimens. While bulk crystals exhibit fractal patterns of purely ferromagnetic domain ordering at room temperature, ultrathin Mn1.4PtSn lamellae clearly show antiskyrmion lattices with lattice spacings up to several mu m. In the paper presented here, we systematically investigate the thickness region from 400 nm to 10 mu m using 100 x 100 mu m(2) wide Mn1.4PtSn plates, and identify the critical thickness-to-width aspect ratio alpha(0) = 0.044 for the ferromagnetic fractal domain to the noncollinear texture phase transition. Additionally, we also explore these noncollinear magnetic textures below the critical aspect ratio alpha(0) above and below the spin-reorientation transition temperature TSR while applying variable external magnetic fields. What we find is a strong hysteresis for the occurrence of an antiskyrmion lattice, since the antiskyrmions preferentially nucleate by pinching them off from helical stripes in the transition to the field polarized state.