Recognition of Flat Orbifolds and the Classification of Tilings in R3
Recognition of Flat Orbifolds and the Classification of Tilings in R3
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R3 中平面 Orbifold 的识别和平铺的分类
DOI：
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发表时间：
2001
影响因子：
0.8
通讯作者：
O. Delgado
中科院分区：
文献类型：
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作者：
O. Delgado
我们讨论的标准orbifold进行平坦的几何形状，即，一个是模仿欧几里德几何，并显示如何导致这些实际的平面度测试在三维的情况下。这在组合平铺理论中有直接的应用，即在三维周期平铺的等变等价分类中，以及在材料科学中。
We discuss criteria for an orbifold to carry a flat geometry, i.e., one which is modelled on euclidean geometry, and show how these lead to a practical flatness test in the three-dimensional case. This has immediate applications in combinatorial tiling theory, namely in the classification of three-dimensional periodic tilings up to equivariant equivalence, and in the material sciences.