On the basis of finite group theory, that by the end of the XIXth century was reaching a firm state of ripeness, the question raised in Sect.  2.2, how many of the Alhambra patterns are possible? could be answered. The man who found the answer, establishing that they are exactly 17, as many as those realized in the decorations of the XIIIth century arabic palace, was the Russian geologist, crystallographer and mathematician Evgar Stepanovich Fyodorov (see Fig. 4.1).