五角反棱柱
正五角反棱柱![五角反棱柱](//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Pentagonal_antiprism.png/240px-Pentagonal_antiprism.png) | 類別 | 反棱柱 柱狀均勻多面體 |
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對偶多面體 | 五方偏方面體 |
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識別 |
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名稱 | 正五角反棱柱 |
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參考索引 | U77(c) |
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鮑爾斯縮寫
| pap![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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數學表示法 |
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考克斯特符號
| ![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) ![10](//upload.wikimedia.org/wikipedia/commons/c/c6/CDel_10.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) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) |
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施萊夫利符號 | s{2,5} |
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威佐夫符號
| | 2 2 5 |
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康威表示法 | A5![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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性質 |
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面 | 12 |
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邊 | 20 |
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頂點 | 10 |
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歐拉特徵數 | F=12, E=20, V=10 (χ=2) |
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組成與佈局 |
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面的種類 | 三角形×10 正五邊形×2 |
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面的佈局
| 10{3}+2{5} |
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頂點圖 | 3.3.3.5 |
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對稱性 |
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對稱群 | D5d, [2+,10], (2*5), order 20 |
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旋轉對稱群
| D5, [5,2]+, (522), order 10 |
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特性 |
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凸 | 圖像 |
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在幾何學中,五角反棱柱又稱為反五角柱或五角反柱是指底為五邊形的反棱柱,側面由三角形組成,若每一個面皆為正多邊形則稱為正五角反棱柱。每個五角反棱柱皆含有12個面,是一種十二面體。
正五角反棱柱是基底為正五邊形的五角反棱柱,其可視為一種半正多面體。
正五角反棱柱也可以視為移除正二十面體底部及頂部的五角錐所構成的立體,因此又稱為正二十面體欠對二側錐。
正五角反棱柱
當底面為正五邊形時,會具備一些特別的性質
當基底邊長為a的時候:
- 頂點數目:10
- 邊數目:20
- 面數目:12
- 對偶多面體:五方偏方面體
- 高:
![{\displaystyle a{\sqrt {{\frac {1}{10}}(5+{\sqrt {5}})}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/569d43100525a2c331e66fd45e9b5ea68cf03c11)
- 表面積:
![{\displaystyle {\frac {1}{2}}a^{2}(5+{\sqrt {3}}+{\sqrt {25+10{\sqrt {5}}}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2192c316fa5618b56b45fcb5253788fe171620ac)
- 體積:
![{\displaystyle {\frac {1}{6}}a^{3}(5+2{\sqrt {5}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f8f672c0bd4896bc894061208be617433c87ad2)
相關多面體與鑲嵌
半正五邊形二面體球面多面體
對稱群:[5,2], (*522)
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[5,2]+, (622)
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.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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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.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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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.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)
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{5,2}
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t{5,2}
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r{5,2}
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2t{5,2}=t{2,5}
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2r{5,2}={2,5}
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rr{5,2}
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tr{5,2}
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sr{5,2}
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半正對偶
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![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.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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![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.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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![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.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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![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![node_fh](//upload.wikimedia.org/wikipedia/commons/6/6f/CDel_node_fh.png) ![5](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png) ![node_fh](//upload.wikimedia.org/wikipedia/commons/6/6f/CDel_node_fh.png) ![2x](//upload.wikimedia.org/wikipedia/commons/1/1c/CDel_2x.png)
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V52
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V102
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V52
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V4.4.5
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V25
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V4.4.5
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V4.4.10
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V3.3.3.5
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半正反棱柱系列
2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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n
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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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作為球面鑲嵌
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參見
外部連結
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