A shoe for a crawler track includes a first end, a second end, a longitudinal axis extending between the first and second ends, a roller path axis extending perpendicular to the longitudinal axis, and an intermediate portion disposed between the first and second ends. The intermediate portion includes a roller-engaging portion disposed along the roller path axis, the intermediate portion including four successive faces that form a parallelogram when viewed from a direction substantially perpendicular to the longitudinal axis, two of the four faces being disposed at an acute angle relative to the longitudinal axis.