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- W1661011193 abstract "This chapter describes the complex exponential in three dimensions. In two dimensions the translation vectors give periodicity directions, and lines interact in the plane to give 2D repetition. The general complex exponential is obtained from the symmetry. It is easy to realize the diamond structure in which each atom is bonded to four others and the structure is also that of cristobalite or cubic ice. It is found that when the constant increases, the small round particles grow into tetrahedral shape and finally join the larger round bodies, each at eight places through catenoids. The larger bodies become cube-like. Each small atom is surrounded by four larger in a tetrahedral manner, which with the catenoids developed is a piece of the D-surface. It is found that the larger bodies are surrounded by eight small ones, giving a shape as a piece of the IWP surface. It is observed that the octahedra go apart, and are only joined by thin tube-like catenoids as an effect of going up in exponential." @default.
- W1661011193 created "2016-06-24" @default.
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- W1661011193 date "1998-01-01" @default.
- W1661011193 modified "2023-09-25" @default.
- W1661011193 title "Periodicity and the Complex Exponential" @default.
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- W1661011193 doi "https://doi.org/10.1016/b978-044482994-8/50003-0" @default.
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