We study piecewise linear density estimators from the L-1 point of view: the frequency polygons investigated by SCOTT (1985) and JONES et al. (1997), and a new piecewise linear histogram. In contrast to the earlier proposals, a unique multivariate generalization of the new piecewise linear histogram is available. All these estimators are shown to be universally L-1 strongly consistent. We derive large deviation inequalities. For twice differentiable densities with compact support their expected L-1 error is shown to have the same rate of convergence as have kernel density estimators. Some simulated examples are presented.