Abstract
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).
\(\chi \alpha \lambda \varepsilon \pi {\grave{\alpha }}\), \(\tau {\grave{\alpha }}\) \(\kappa \alpha \lambda \acute{\alpha }\)
Nothing beautiful without struggle.
Plato
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This movement was an offspring of Zemlya i Volya.
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Plato, Respub \(530^{d}1\).
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- 4.
The result of performing the exchange of the rows with the columns of a matrix A is a new matrix \(A^T\), named the transpose of the previous one. The element \(A^T_{ij}\) of the transposed matrix is equal to \(A_{ji}\) of the original one.
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In fomulae the elements of the hermitian conjugate matrix \(\mathscr {U}^\star \) are as follows \(\mathscr {U}^\dagger _{ij} = \mathscr {U}_{ji}^\star \).
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Fré, P.G. (2018). From Crystals to Plato. In: A Conceptual History of Space and Symmetry . Springer, Cham. https://doi.org/10.1007/978-3-319-98023-2_4
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