A new class of integer polyhedra with box-tdi systems, called switchde
c polyhedra, is introduced. They involve families of {0, +/-1}-vectors
associated to abstract paths and circuits, which are in a certain sen
se closed under ''switching'' and ''decomposition''. The switchdec pol
yhedra generalize and unify previous models, like the coflow polyhedra
, most of the switching paths polyhedra of Groflin (which generalize t
he switching model of Hoffman) and examples like the polyhedral descri
ption of dicuts.