  The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained
using exact diagonalization of systems with up to 26 spins and by density
matrix renormalization group calculations to 500 spins. The ladders have
isotropic antiferromagnetic (AF) exchange $J_2 > 0$ between first neighbors in
the legs, variable isotropic AF exchange $J_1$ between some first neighbors in
different legs, and an unpaired spin per odd-membered ring when $J_1 \gg J_2$.
Ladders with skewed rungs and variable $J_1$ have frustrated AF interactions
leading to multiple quantum phases: AF at small $J_1$, either F or AF at large
$J_1$, as well as bond-order-wave phases or reentrant AF (singlet) phases at
intermediate $J_1$.
