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Heliogravure--is a fairly obscure printing process, and it is just about as complicated as it is hard to pronounce. Essentially it is a process of photoengraving, sometimes called photogravure. An original image is transferred to a photosensitive film or gel using a large flash of light. This image is then transferred to a (usually) copper plate. The copper plate is then sent through one or more chemical baths which etches the image into the plate. The plate is dried, buffed, and polished. When it is finally ready, ink is applied over the plate and it is run (with paper or canvas) through a press. In the case of Dali's Alice in Wonderland, the plates were inked multiple times to transfer various colors onto one image.
If you have a couple of minutes, take a gander at this youtube video. He does a very nice job showing the process from start to finish.