The pion spectra of the decay K20-->π++π- +π0 are presented. Results are based on 1198 Kπ30 decays that were recorded with a spark chamber setup. Kπ30 is well described by a linear matrix element of the form M~1+σ0'[2T(π0)- T(π0)] mkmπ2 with σ0'=-0.21+/-0.02. There is no observable dependence of the matrix element on the X variable, X~[T(π+)-T(π-)]. Our measurement is in agreement with the |∆I|=12 rule. Various models to explain the observed variation of the density of the Dalitz plot are discussed. The value for the slope parameter is in good agreement with certain speculative predictions based on equal-time current commutators. No evidence for CP violation is found.