This report discusses the optimization strategy, the theoretical background and first experimental data of a new refractive lens for focusing X-rays. In order to reduce the absorption of X-rays in this transmission lens, optically passive material was removed from the necessarily concave lens shape in a highly regular pattern. The feature dimensions require lens production and replication by deep X-ray lithography, which allows shaping in only one dimension. Consequently such a lens can focus in one direction only, so a crossed lens pair is needed for two-dimensional focusing. The single lens is composed of two large prisms of millimetre size, which touch each other at one of the tips, like an old sand clock. Each large prism contains a highly regular structure of essentially identical prism-like smaller segments. The first lens prototypes focused an X-ray beam with a vertical size of 500 microm and a photon energy of 8 keV to a line with a width of only 2.8 microm. This is only slightly worse than the line width of 1.73 microm expected for its focal length of f = 2.18 m. The photon density enhancement in the focus was 25, but could have been larger as the lens can intercept a beam height of 2.6 mm.