在几何学中,七角反棱柱又称为反七角柱或七角反柱是指底为七边形的反棱柱,侧面由三角形组成,若每一个面皆为正多边形则称为正七角反棱柱。每个七角反棱柱皆含有16个面[1][2][3],是一种十六面体。
Quick Facts 类别, 对偶多面体 ...
正七角反棱柱![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Antiprism_7.png/240px-Antiprism_7.png) |
类别 | 反棱柱 柱状均匀多面体 |
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对偶多面体 | 七方偏方面体 |
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名称 | 正七角反棱柱 |
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参考索引 | U77(e) |
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鲍尔斯缩写
| heap![在维基数据编辑](//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png) |
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考克斯特符号
| ![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![2x](//upload.wikimedia.org/wikipedia/commons/1/1c/CDel_2x.png) ![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![14](//upload.wikimedia.org/wikipedia/commons/3/3a/CDel_14.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png)
![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![2x](//upload.wikimedia.org/wikipedia/commons/1/1c/CDel_2x.png) ![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![7](//upload.wikimedia.org/wikipedia/commons/f/fc/CDel_7.png) ![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) |
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施莱夫利符号 | sr{2,7} |
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威佐夫符号
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康威表示法 | A7![在维基数据编辑](//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png) |
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面 | 16 |
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边 | 28 |
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顶点 | 14 |
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欧拉特征数 | F=16, E=28, V=14 (χ=2) |
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面的种类 | 14个三角形 2个正七边形 |
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面的布局
| 14{3}+2{7} |
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顶点图 | 3.3.3.7 |
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对称群 | D7d, [2+,14], (2*7), order 28 |
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旋转对称群
| D7, [7,2]+, (722), order 14 |
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Close
正七角反棱柱是基底为正七边形的七角反棱柱,其可视为一种半正多面体,施莱夫利符号s{2,7}表示其可以借由七边形二面体透过扭棱变换构造。其具有D7对称群[4],其在威佐夫符号中用| 2 2 7表示[5]。
当底面为正七边形时,会具备一些特别的性质
当基底边长为a的时候:
高:![{\displaystyle {\frac {1}{2}}a{\sqrt {4-\sec {\frac {\pi }{14}}\sec {\frac {\pi }{14}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/48fab2e2617d8a0a48698dd1237ebc7eee1f027b)
表面积:![{\displaystyle {\frac {7}{2}}a^{2}(\cot {\frac {\pi }{7}}+{\sqrt {3}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/74555918f1e26462d04244555a399ed7403d7ee2)
体积:
More information [7,2]+, (722), 半正对偶 ...
半正七边形二面体球面多面体
对称群:[7,2], (*722)
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[7,2]+, (722)
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![7](//upload.wikimedia.org/wikipedia/commons/f/fc/CDel_7.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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{7,2}
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t{7,2}
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r{7,2}
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2t{7,2}=t{2,7}
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2r{7,2}={2,7}
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rr{7,2}
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tr{7,2}
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sr{7,2}
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半正对偶
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![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![7](//upload.wikimedia.org/wikipedia/commons/f/fc/CDel_7.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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V72
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V142
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V72
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V4.4.7
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V27
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V4.4.7
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V4.4.14
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V3.3.3.7
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More information n, s{2,4} sr{2,2} ...
半正反棱柱系列
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s{2,4} sr{2,2}
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s{2,6} sr{2,3}
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s{2,8} sr{2,4}
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s{2,10} sr{2,5}
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s{2,12} sr{2,6}
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s{2,14} sr{2,7}
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s{2,16} sr{2,8}
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s{2,18} sr{2,9}
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s{2,20} sr{2,10}
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s{2,22} sr{2,11}
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s{2,24} sr{2,12}
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s{2,2n} sr{2,n}
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![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![2x](//upload.wikimedia.org/wikipedia/commons/1/1c/CDel_2x.png) ![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png)
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作为球面镶嵌
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Melnyk, Theodor William, Osvald Knop, and William Robert Smith. "Extremal arrangements of points and unit charges on a sphere: equilibrium configurations revisited." Canadian Journal of Chemistry 55.10 (1977): 1745-1761.
- Fowler, P. W., T. Tarnai, and Zs Gáspár. "From circle packing to covering on a sphere with antipodal constraints." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458.2025 (2002): 2275-2287.
- heptagonal antiprism(页面存档备份,存于互联网档案馆) rediff.com [2014-6-22]