Symmetry relations in charmless B->PPP decays

Strangeness-changing decays of $B$ mesons to three-body final states of pions and kaons are studied, assuming that they are dominated by a $\Delta I=0$ penguin amplitude with flavor structure $\bar b \to \bar s$. Numerous isospin relations for $B\to K\pi\pi$ and for underlying quasi-two-body decays are compared successfully with experiment, in some cases resolving ambiguities in fitting resonance parameters. The only exception is a somewhat small branching ratio noted in $B^0\to K^{*0}\pi^0$, interpreted in terms of destructive interference between a penguin amplitude and an enhanced electroweak penguin contribution. Relations for B decays into three kaons are derived in terms of final states involving $K_S$ or $K_L$, assuming that $\phi K$-subtracted decay amplitudes are symmetric in $K$ and $\bar K$, as has been observed experimentally. Rates due to nonresonant backgrounds are studied using a simple model, which may reduce discrete ambiguities in Dalitz plot analyses.