正多边形 (在二维中)、多面体 (三维中)或 多胞形 ( 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 。
恰好有三种正镶嵌 是由对称地铺满平面的正多边形组成。
由两个或多个 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)。
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 和截角八面体 。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。
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 ,
胞 ,
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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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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