在幾何學中,大斜方截半立方體堆砌(英語:Cantitruncated cubic honeycomb)是一種歐幾里得三維空間的半正堆砌,是由大斜方截半立方體、截角八面體和正方體以1:1:3的比例堆砌而成。
Quick Facts 大斜方截半立方體堆砌, 類型 ...
大斜方截半立方體堆砌 |
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![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/HC_A6-A4-P2.png/220px-HC_A6-A4-P2.png) |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Cantitruncated_cubic_tiling.png/220px-Cantitruncated_cubic_tiling.png) 線架圖 |
類型 | 均勻堆砌 |
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維度 | 3 |
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對偶多胞形 | triangular pyramidille |
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考克斯特符號
| ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![3](//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png)
![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![split1](//upload.wikimedia.org/wikipedia/commons/a/a1/CDel_split1.png) = ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![3](//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_h0](//upload.wikimedia.org/wikipedia/commons/5/5d/CDel_node_h0.png) |
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纖維流形記號 | 4−:2 |
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施萊夫利符號 | tr{4,3,4} t0,1,2{4,3,4} |
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胞 | t {3 4} ![](//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Great_rhombicuboctahedron.png/20px-Great_rhombicuboctahedron.png) t {3,4} ![](//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Truncated_octahedron.png/20px-Truncated_octahedron.png) {4,3} ![](//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/20px-Hexahedron.png) |
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面 | {4} ![](//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Kvadrato.svg/20px-Kvadrato.svg.png) {6} ![](//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Regular_hexagon.svg/20px-Regular_hexagon.svg.png) {8} ![](//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/O%C5%9Bmiok%C4%85t_foremny.PNG/20px-O%C5%9Bmiok%C4%85t_foremny.PNG) |
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頂點圖 | ![](//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Cantitruncated_cubic_honeycomb_verf.png/50px-Cantitruncated_cubic_honeycomb_verf.png) ![](//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Omnitruncated_alternated_cubic_honeycomb_verf.png/50px-Omnitruncated_alternated_cubic_honeycomb_verf.png) (Irreg. 正四面體) |
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對稱群 | ![{\displaystyle {\tilde {C}}_{4}}](//wikimedia.org/api/rest_v1/media/math/render/svg/404d24500dbc31cb7df8b26172d5e64d2f7b09cb) |
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空間群 | Pm3m (221) |
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考克斯特群 | [4,3,4], ![{\displaystyle {\tilde {C}}_{3}}](//wikimedia.org/api/rest_v1/media/math/render/svg/58f6155c77ccc8f6acc9a64d6b2d78e025897f6e) |
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頂點正 |
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Close
康威稱大斜方截半立方體堆砌為n-tCO-trille[1]。
大斜方截半立方體堆砌應該解釋為「大斜方截角,立方體堆砌」,即對立方體堆砌進行高維度之大斜方操作(Cantitruncated)而成之幾何體
四個胞周圍的每個頂點的形式為:
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/2/26/2-Kuboktaederstumpf_1-Oktaederstumpf_1-Hexaeder.png/640px-2-Kuboktaederstumpf_1-Oktaederstumpf_1-Hexaeder.png)
每個頂點皆由2個大斜方截半立方體、1個截角八面體以及1個正方體所組成。
該幾何體存在兩種不同對稱性的表面塗色。線性考克斯特圖的形式可以得出同一種表面塗色每個胞的類型。分岔圖的形式,可以得出兩種類型的大斜方截半立方體有序的胞(顏色)交替。
More information [4,3,4],
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結構
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大斜方截角立方
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大斜方截半交錯立方
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考克斯特群
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[4,3,4], ![{\displaystyle {\tilde {C}}_{3}}](//wikimedia.org/api/rest_v1/media/math/render/svg/58f6155c77ccc8f6acc9a64d6b2d78e025897f6e) =<[4,31,1]>
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[4,31,1],
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空間群 |
Pm3m (221) |
Fm3m (225)
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Fibrifold |
4−:2 |
2−:2
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表面塗色
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考克斯特標記
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![3](//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![split1](//upload.wikimedia.org/wikipedia/commons/a/a1/CDel_split1.png)
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頂點圖
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頂點 值 對稱群
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[ ] order 2
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[ ]+ order 1
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- George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (包含11個凸半正鑲嵌、28個凸半正堆砌、和143個凸半正四維砌的全表)
- Kaleidoscopes: Selected Writings of H.S.M. Coxeter, F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication參與編輯, 1995, ISBN 978-0-471-01003-6 [1](頁面存檔備份,存於網際網路檔案館)
- (22頁) H.S.M.考克斯特, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 半正空間鑲嵌)
- A. Andreini, Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative (On the regular and semiregular nets of polyhedra and on the corresponding correlative nets), Mem. Società Italiana della Scienze, Ser.3, 14 (1905) 75–129.
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, Architectonic and Catoptric tessellations, p 292-298, includes all the nonprismatic forms)