在几何学中,六角反棱柱又称为反六角柱或六角反柱是指底为六边形的反棱柱,侧面由三角形组成,若每一个面皆为正多边形则称为正六角反棱柱。每个六角反棱柱皆含有14个面,是一种十四面体。
Quick Facts 类别, 对偶多面体 ...
正六角反棱柱![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Hexagonal_antiprism.png/240px-Hexagonal_antiprism.png) |
类别 | 反棱柱 柱状均匀多面体 |
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对偶多面体 | 六方偏方面体 |
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名称 | 正六角反棱柱 |
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参考索引 | U77(d) |
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鲍尔斯缩写
| hap![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) ![12](//upload.wikimedia.org/wikipedia/commons/0/0e/CDel_12.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) |
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施莱夫利符号 | s{2,6} |
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威佐夫符号
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康威表示法 | A6![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 | 14 |
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边 | 24 |
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顶点 | 12 |
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欧拉特征数 | F=14, E=24, V=12 (χ=2) |
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面的种类 | 三角形×12 正六边形×2 |
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顶点图 | 3.3.3.6 |
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对称群 | D6d, [2+,12], (2*6), order 24 |
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旋转对称群
| D6, [6,2]+, (622), order 12 |
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Close
正六角反棱柱是基底为正六边形的六角反棱柱,其可视为一种半正多面体。
当一个六角反棱柱的底面为正六边形且侧面为正三角形时,会具备一些特别的性质:
当基底边长为a的时候:
- 顶点数目:12
- 边数目:24
- 面数目:14
- 对偶多面体:六方偏方面体
- 高:
![{\displaystyle a{\sqrt {{\sqrt {3}}-1}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/07681fb3d7982b92f2adc34291b12a1722b2ca6d)
- 表面积:
![{\displaystyle 6a^{2}{\sqrt {3}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/03505e05791f6735f70ce127c14f93884c39372e)
- 体积:
![{\displaystyle a^{3}{\sqrt {2(1+{\sqrt {3}}}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/ad7d37b26f99a1b0523a6f448f5d1696e9b9a328)
More information [6,2]+, (622), [1+,6,2], (322) ...
半正六边形二面体球面多面体
对称群:[6,2], (*622)
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[6,2]+, (622)
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[1+,6,2], (322)
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[6,2+], (2*3)
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{6,2}
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t{6,2}
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r{6,2}
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2t{6,2}=t{2,6}
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2r{6,2}={2,6}
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rr{6,2}
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tr{6,2}
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sr{6,2}
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h{6,2}
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s{2,6}
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半正对偶
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V62
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V122
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V62
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V4.4.6
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V26
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V4.4.6
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V4.4.12
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V3.3.3.6
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V32
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V3.3.3.3
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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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