在幾何學中,截對角偏方面體是一種多面體,可以透過將偏方面體截去上下兩個頂點構成,並具備二面體群對稱性[1]。它的命名方式是根據上下兩個面的形狀而命名的,例如:正十二面體可以視為是截對角正五方偏方面體,它的上下兩個面都是正五邊形,其他的面也是五邊形;[2]:251截對角四方偏方面體的上下兩個面則是正方形或四邊形,其他的面則是五邊形,依此類推。部分的截對角偏方面體可以作為化學的分子籠結構。[3]
事实速览 類別, 對偶多面體 ...
截對角偏方面體![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Pentagonal_truncated_trapezohedron.png/240px-Pentagonal_truncated_trapezohedron.png) 以正十二面體作為截對角五方偏方面體為例 |
類別 | 截對角偏方面體 |
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對偶多面體 | 雙錐反柱體 |
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面 | ![{\displaystyle {{{2}\,{n}}+{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/be4c4e14c0487ae986b691e2ba6ae819e034ddca) |
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邊 | ![{\displaystyle {{6}\,{n}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/bf914d3ba32061cecb5e906ea109a7d318be2944) |
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頂點 | ![{\displaystyle {{4}\,{n}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a93d63efdca3f2748c17395532ea00c855d060e2) |
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歐拉特徵數 | F= , E= , V= (χ=2) |
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面的種類 | 2n個五邊形,2個n邊形 |
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對稱群 | Dnd, [2+,2n], (2*n), 階數 4n |
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旋轉對稱群
| Dn, [2,2n]+, (22n), 階數 2n |
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|
凸 |
註: 為底面邊數 。 |
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关闭
Katrina Biele, Yuan Feng, David Heras, Ahmed Tadde. Associating Finite Groups with Dessins d’Enfants (PDF). Purdue Research in Mathematics Experience (PRiME), Department of Mathematics, Purdue University. 2013 [2021-10-23]. (原始内容存档 (PDF)于2021-10-23).
Alsina, C. and Nelsen, R.B. A Mathematical Space Odyssey: Solid Geometry in the 21st Century. Dolciani Mathematical Expositions. Mathematical Association of America. 2015. ISBN 9781614442165.
Weitzel, Hans, A further hypothesis on the polyhedron of A. Dürer's engraving Melencolia I, Historia Mathematica, 2004, 31 (1): 11–14, doi:10.1016/S0315-0860(03)00029-6 ![可免费查阅](//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png)
Diudea, M.V. and Nagy, C.L. Diamond and Related Nanostructures. Carbon Materials: Chemistry and Physics. Springer Netherlands. 2013. ISBN 9789400763715.
Wang, Dong and Cherkaev, Andrej and Osting, Braxton. Dynamics and stationary configurations of heterogeneous foams. PloS one (Public Library of Science). 2019, 14 (4): e0215836.
Șerban, D. A., Sărăndan, S., Negru, R., Belgiu, G., & Marşavina, L., A Parametric Study of the Mechanical Properties of Open-Cell Kelvin Structures, IOP Conference Series: Materials Science and Engineering 416 (1) (IOP Publishing), 2018, 416 (1): 012108