Modern nanotechnology offers routes to create new artificial materials, widening the functionality of devices in physics, chemistry, and biology. Templated self-organization has been recognized as a possible route to achieve exact positioning of quantum dots to create quantum dot arrays, molecules, and crystals. Here we employ extreme ultraviolet interference lithography (EUV-IL) at a wavelength of lambda = 13.5 nm for fast, large-area exposure of templates with perfect periodicity. Si(001) substrates have been patterned with two-dimensional hole arrays using EUV-IL and reactive ion etching. On these substrates, three-dimensionally ordered SiGe quantum dot crystals with the so far smallest quantum dot sizes and periods both in lateral and vertical directions have been grown by molecular beam epitaxy. X-ray diffractometry from a sample volume corresponding to about 3.6 x 10(7) dots and atomic force microscopy (AFM) reveal an up to now unmatched structural perfection of the quantum dot crystal and a narrow quantum dot size distribution. Intense interband photoluminescence has been observed up to room temperature, indicating a low defect density in the three-dimensional (3D) SiGe quantum dot crystals. Using the Ge concentration and dot shapes determined by X-ray and AFM measurements as input parameters for 3D band structure calculations, an excellent quantitative agreement between measured and calculated PL energies is obtained. The calculations show that the band structure of the 3D ordered quantum dot crystal is significantly modified by the artificial periodicity. A calculation of the variation of the eigenenergies based on the statistical variation in the dot dimensions as determined experimentally (+/-10% in linear dimensions) shows that the calculated electronic coupling between neighboring dots is not destroyed due to the quantum dot size variations. Thus, not only from a structural point of view but also with respect to the band structure, the 3D ordered quantum dots can be regarded as artificial crystal.