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Titlebook: Geometric Crystallography; An Axiomatic Introdu Peter Engel Book 1986 D. Reidel Publishing Company, Dordrecht, Holland 1986 crystal.crystal

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书目名称Geometric Crystallography
副标题An Axiomatic Introdu
编辑Peter Engel
视频video
图书封面Titlebook: Geometric Crystallography; An Axiomatic Introdu Peter Engel Book 1986 D. Reidel Publishing Company, Dordrecht, Holland 1986 crystal.crystal
描述In the last decade mathematical crystallography has found increasing interest. Siginificant results have been obtained by algebraic, geometric, and group theoretic methods. Also classical crystallography in three-dimen­ sional Euclidean space has been extended to higher dimen­ sions in order to understand better the dimension independent crystallographic properties. The aim of this note is to introduce the reader to the fascinating and rich world of geometric crystallography. The prerequisites for reading it are elementary geometry and topological notations, and basic knowledge of group theory and linear algebra. Crystallography is geometric by its nature. In many cases, geometric arguments are the most appropriate and can thus best be understood. Thus the geometric point of view is emphasized here. The approach is axiomatic start­ ing from discrete point sets in Euclidean space. Symmetry comes in very soon and plays a central role. Each chapter starts with the necessary definitions and then the subject is treated in two- and three-dimensional space. Subsequent sections give an extension to higher dimensions. Short historical remarks added at the end of the chapters will show the d
出版日期Book 1986
关键词crystal; crystallography; point group; polytope
版次1
doihttps://doi.org/10.1007/978-94-009-4760-3
isbn_softcover978-90-277-2341-3
isbn_ebook978-94-009-4760-3
copyrightD. Reidel Publishing Company, Dordrecht, Holland 1986
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978-90-277-2341-3D. Reidel Publishing Company, Dordrecht, Holland 1986
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For applications it is important to decide wether two different lattice bases belong to one and the same lattice T.. This problem is solved through the determination of an integral reduced form denoted here as ℤ-reduced.
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The Old Order and Its Discontents,We now use the important concept of a mathematical group. The group elements are the symmetry operations. The group multiplication is the composition of symmetry operations as described in section 1.4.
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Siemens-Design Grundlagen und Perspektiven,Up till now symmetry groups were considered only which leave at least one point fixed. This restriction is now removed and we investigate groups of symmetry operations which act transitively on a regular point system XCE..
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