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镶嵌


正多边形(在二维中)、多面体(三维中)或 多胞形n 维)的铺砖称为镶嵌。镶嵌可以使用施莱夫利符号来指定。

将自相交多边形分解成简单多边形也称为镶嵌 (Woo et al. 1999),或更准确地说,称为多边形镶嵌

RegularTessellations

恰好有三种正镶嵌是由对称地铺满平面的正多边形组成。

SemiregularTessellations

两个或多个凸正多边形对平面进行镶嵌,使得相同的多边形以相同的顺序围绕每个多边形顶点,称为半正镶嵌,有时也称为阿基米德镶嵌。在平面上,有八种这样的镶嵌,如上图所示(Ghyka 1977, pp. 76-78; Williams 1979, pp. 37-41; Steinhaus 1999, pp. 78-82; Wells 1991, pp. 226-227)。

DemiregularTessellations

有 14 种准正(或多态)镶嵌,它们是由三个正镶嵌和八个半正镶嵌有序组合而成(Critchlow 1970, pp. 62-67; Ghyka 1977, pp. 78-80; Williams 1979, p. 43; Steinhaus 1999, pp. 79 和 81-82)。

在三维中,能够镶嵌空间的多面体称为空间填充多面体。例子包括立方体菱形十二面体截角八面体。还有一种 16 面的空间填充物和一个凸多面体,称为Schmitt-Conway 双棱柱,它仅非周期性地填充空间。

n 维多胞形的镶嵌称为蜂巢


另请参阅

阿基米德立体, 开罗镶嵌, , 准正镶嵌, 对偶镶嵌, 六边形网格, 铰链镶嵌, 蜂巢, 蜂巢猜想, 开普勒怪物, 正镶嵌, 施莱夫利符号, 半正多面体, 半正镶嵌, 空间填充多面体, 螺旋相似性, 正方形网格, 对称性, 铺砖, 三角形网格, 三角对称群, 三角剖分, 壁纸群

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参考文献

Ball, W. W. R. 和 Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 105-107, 1987.Bhushan, A.; Kay, K.; 和 Williams, E. "Totally Tessellated." http://library.thinkquest.org/16661/.Britton, J. Symmetry and Tessellations: Investigating Patterns. Englewood Cliffs, NJ: Prentice-Hall, 1999.Critchlow, K. Order in Space: A Design Source Book. New York: Viking Press, 1970.Cundy, H. 和 Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 60-63, 1989.Gardner, M. Martin Gardner's New Mathematical Diversions from Scientific American. New York: Simon and Schuster, pp. 201-203, 1966.Gardner, M. "Tilings with Convex Polygons." Ch. 13 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, pp. 162-176, 1988.Ghyka, M. The Geometry of Art and Life. New York: Dover, 1977.Kraitchik, M. "Mosaics." §8.2 in Mathematical Recreations. New York: W. W. Norton, pp. 199-207, 1942.Lines, L. Solid Geometry, with Chapters on Space-Lattices, Sphere-Packs, and Crystals. New York: Dover, pp. 199 和 204-207 1965.Pappas, T. "Tessellations." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 120-122, 1989.Peterson, I. The Mathematical Tourist: Snapshots of Modern Mathematics. New York: W. H. Freeman, p. 75, 1988.Radin, C. Miles of Tiles. Providence, RI: Amer. Math. Soc., 1999.Rawles, B. Sacred Geometry Design Sourcebook: Universal Dimensional Patterns. Nevada City, CA: Elysian Pub., 1997.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 75-76 和 78-82, 1999.Vichera, M. "Archimedean Polyhedra." http://www.vicher.cz/puzzle/telesa/telesa.htm.Walsh, T. R. S. "Characterizing the Vertex Neighbourhoods of Semi-Regular Polyhedra." Geometriae Dedicata 1, 117-123, 1972.Weisstein, E. W. "Books about Tilings." http://www.ericweisstein.com/encyclopedias/books/Tilings.html.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 121, 213, 和 226-227, 1991.Williams, R. The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover, pp. 35-43, 1979.Woo, M.; Neider, J.; Davis, T.; 和 Shreiner, D. Ch. 11 in OpenGL 1.2 Programming Guide, 3rd ed.: The Official Guide to Learning OpenGL, Version 1.2. Reading, MA: Addison-Wesley, 1999.

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镶嵌

引用为

Weisstein, Eric W. "镶嵌." 来自 MathWorld--Wolfram Web 资源. https://mathworld.net.cn/Tessellation.html

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