Moving rectangular sofas in planar and spatial corridors

We consider eight natural planar corridors, including the standard $\mathrm{L}$-shaped one, and characterize the rectangles that can move around their corners. As a bi-product we describe completely the corresponding rectangles with maximum area, as well as the rectangular parallelepipeds with maximum volume that can move around the corners of the spatial analogues of the considered eight planar corridors.