在几何学中,正八边形镶嵌(英语:Octagonal tiling)是一种由正八边形拼合,并且将正八边形重复排列组合,并让图形完全拼合,而且没有空隙或重叠的几何构造,每个顶点皆为三个正八边形的公共顶点,以顶点图8.8.8或83表示。
正八边形镶嵌是一种双曲正镶嵌,在施莱夫利符号中用{8,3}表示。
表面涂色
就如同平面上的正六边形镶嵌,正八边形镶嵌也具有3种不同的半正表面涂色,都可以由威佐夫结构面对称构造出来。(h,k)表示一种表面涂色的面周期性重复,以正八边形距离h、k计数,h在前、k在后。
相关多面体及镶嵌
{8,2} |
{8,3} |
{8,4} |
{8,5} |
{8,6} |
{8,7} |
{8,8} |
... | {8,∞} |
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参见
参考文献
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
- Chapter 10: Regular honeycombs in hyperbolic space. The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.
外部链接
- 埃里克·韦斯坦因. Hyperbolic tiling. MathWorld.
- 埃里克·韦斯坦因. Poincaré hyperbolic disk. MathWorld.
- Hyperbolic and Spherical Tiling Gallery (页面存档备份,存于互联网档案馆)
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings (页面存档备份,存于互联网档案馆)
- Hyperbolic Planar Tessellations, Don Hatch (页面存档备份,存于互联网档案馆)
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