Amplitude analysis of the decays <i>D</i><SUP>0</SUP> → π<SUP>+</SUP>π<SUP>-</SUP>π<SUP>+</SUP>π<SUP>-</SUP> and <i>D</i><SUP>0</SUP> → π<SUP>+</SUP>π<SUP>-</SUP>π<SUP>0</SUP>π<SUP>0</SUP>

Using e(+)e(-) annihilation data corresponding to an integrated luminosity of 2.93 fb(-1) taken at the center-of-mass energy root s = 3.773 GeV with the BESIII detector, a joint amplitude analysis is performed on the decays D-0 -> pi(+)pi(-)pi(+)pi(-) and D-0 -> pi(+)pi(-)pi(0)pi(0) (non-eta). The fit fractions of individual components are obtained, and large interferences among the dominant components of the decays D-0 -> alpha(1)(1260)pi, D-0 -> pi(1300)pi, D-0 -> rho(770)rho(770), and D-0 -> 2(pi pi)(s) are observed in both channels. With the obtained amplitude model, the CP-even fractions of D-0 -> pi(+)pi(-)pi(+)pi(-) and D-0 -> pi(+)pi(-)pi(0)pi(0) (non-eta) are determined to be (75.2 +/- 1.1(stat.) +/- 1.5(syst))% and (68.9 +/- 1.5(stat.) +/- 2.4(syst.))%, respectively. The branching fractions of D-0 -> pi(+)pi(-)pi(+)pi(-) and D-0 -> pi(+)pi(-)pi(0)pi(0) (non-eta) are measured to be (0.688 +/- 0.010(stat). +/- 0.010(syst.)) % and (0.951 +/- 0.025(stat.) +/- 0.021(syst.))%, respectively. The amplitude analysis provides an important model for the binning strategy in measuring the strong phase parameters of D-0 -> 4 pi when used to determine the CKM angle gamma(phi(3)) via the B- -> DK- decay.