# 多邊形二面體

類別 多邊形二面體的例子：球面上的六邊形二面體 均勻多面體球面鑲嵌 多面形 .mw-parser-output .CDD-invert img{filter:invert(100%)}.mw-parser-output .CDD-white img{filter:contrast(0)brightness(100)}.mw-parser-output .CDD-red img{filter:brightness(0%)contrast(0%)sepia(100%)saturate(1000)}.mw-parser-output .CDD-yellow img{filter:brightness(0%)contrast(0%)sepia(100%)saturate(15)hue-rotate(30deg)saturate(10)}.mw-parser-output .CDD-orange img{filter:brightness(0%)contrast(0%)sepia(100%)saturate(10)}.mw-parser-output .CDD-green img{filter:brightness(0%)contrast(0%)sepia(100%)saturate(1000)hue-rotate(120deg)}.mw-parser-output .CDD-cyan img{filter:brightness(0%)contrast(0%)sepia(100%)saturate(15)hue-rotate(180deg)saturate(10)}.mw-parser-output .CDD-blue img{filter:brightness(0%)contrast(0%)sepia(100%)saturate(1000)hue-rotate(-120deg)}.mw-parser-output .CDD-purple img{filter:brightness(0%)contrast(0%)sepia(100%)saturate(15)hue-rotate(-140deg)saturate(10)} {n,2} 2 | n 2 ${\displaystyle 2}$ ${\displaystyle n}$ ${\displaystyle n}$ F=${\displaystyle 2}$, E=${\displaystyle n}$, V=${\displaystyle n}$ （χ=2） .mw-parser-output .serif{font-family:Times,serif}n邊形 n2 Dnh, [2,n], (*22n), order 4n Dn, [2,n]+, (22n), order 2n 註：${\displaystyle n}$為底面邊數 。 .mw-parser-output .hlist ul,.mw-parser-output .hlist ol{padding-left:0}.mw-parser-output .hlist li,.mw-parser-output .hlist dd,.mw-parser-output .hlist dt{margin:0;display:inline}.mw-parser-output .hlist dt:after,.mw-parser-output .hlist dd:after,.mw-parser-output .hlist li:after{white-space:normal}.mw-parser-output .hlist dt:after{content:" :"}.mw-parser-output .hlist dd:after,.mw-parser-output .hlist li:after{content:" · ";font-weight:bold}.mw-parser-output .hlist-pipe dd:after,.mw-parser-output .hlist-pipe li:after{content:" | ";font-weight:normal}.mw-parser-output .hlist-hyphen dd:after,.mw-parser-output .hlist-hyphen li:after{content:" - ";font-weight:normal}.mw-parser-output .hlist-comma dd:after,.mw-parser-output .hlist-comma li:after{content:"、";font-weight:normal}.mw-parser-output .hlist dd:last-child:after,.mw-parser-output .hlist dt:last-child:after,.mw-parser-output .hlist li:last-child:after{content:none}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li:before{content:" "counter(listitem)" ";white-space:nowrap}.mw-parser-output .hlist dd ol>li:first-child:before,.mw-parser-output .hlist dt ol>li:first-child:before,.mw-parser-output .hlist li ol>li:first-child:before{content:" ("counter(listitem)" "}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li:before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child:before,.mw-parser-output .hlist dt ol>li:first-child:before,.mw-parser-output .hlist li ol>li:first-child:before{content:" ("counter(listitem)"\a0 "}.mw-parser-output ul.cslist,.mw-parser-output ul.sslist{margin:0;padding:0;display:inline-block;list-style:none}.mw-parser-output .cslist li,.mw-parser-output .sslist li{margin:0;display:inline-block}.mw-parser-output .cslist li:after{content:"，"}.mw-parser-output .sslist li:after{content:"；"}.mw-parser-output .cslist li:last-child:after,.mw-parser-output .sslist li:last-child:after{content:none}.mw-parser-output .navbar{display:inline;font-weight:normal;font-size:88%}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit;color:inherit!important}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}

n邊形二面體的對偶多面體n面形，由n二角形共用兩個頂點組成。

## 作為球面鑲嵌

2 {0} 2 {1} 2 {2} 2 {3} 2 {4} 2 {5} 2 {6} ... 2 {∞}

0個頂點
1條邊
1 2 3 4 5 6 ...

{1,2}

{2,2}

{3,2}

{4,2}

{5,2}

{6,2}

{7,2}

{8,2}
...

{∞,2}

{iπ/λ,2}

## 註釋

1. ^ 根據核殼層結構論文，其指出零面體這種結構有2個頂點、1條邊和0個面[8]，依照對偶多面體的定義，面和頂點將交換，零面體的對偶多面體將會存在0個頂點、1條邊和2個面，這種結構可以視作是一種多邊形二面體的球面鑲嵌，由一條邊將球面分割成2個面，但不存在頂點，因此其面可以視為是一種0個頂點和1條邊組成的零角形，所對應的幾何結構為零角形二面體

## 參考文獻

1. ^ Gausmann, Evelise; Roland Lehoucq, Jean-Pierre Luminet, Jean-Philippe Uzan, Jeffrey Weeks. Topological Lensing in Spherical Spaces. Classical and Quantum Gravity. 2001, 18: 5155–5186. . doi:10.1088/0264-9381/18/23/311.
2. ^ Kántor, S., On the volume of unbounded polyhedra in the hyperbolic space (PDF), Beiträge zur Algebra und Geometrie, 2003, 44 (1): 145–154 [2017-02-14], MR 1990989, （原始内容 (PDF)存档于2017-02-15）.
3. O'Rourke, Joseph, Flat zipper-unfolding pairs for Platonic solids, 2010, Bibcode:2010arXiv1010.2450O,
4. ^ Weisstein, Eric W. (编). Dihedron. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
5. ^ Draghicescu, Mircea. Building Polyhedra Models for Mathematical Art Projects and Teaching Geometry (PDF). Proceedings of Bridges 2019: Mathematics, Art, Music, Architecture, Education, Culture. 2019: 629–634 [2022-12-28]. （原始内容存档 (PDF)于2022-12-23）.
6. ^ O'Rourke, Joseph, On flat polyhedra deriving from Alexandrov's theorem, 2010, Bibcode:2010arXiv1007.2016O,
7. ^ Coxeter, H. S. M., Regular Polytopes 3rd, Dover Publications Inc.: 12, January 1973, ISBN 0-486-61480-8
8. ^ G. S. Anagnostatos. On the Possible Stability of Tetraneutron and Hexaneutron. HNPS Proceedings. 2020-02-20, 13: 313 [2021-08-12]. ISSN 2654-0088. doi:10.12681/hnps.2981. （原始内容存档于2021-08-12）.
9. ^ McMullen, Peter; Schulte, Egon, Abstract Regular Polytopes 1st, Cambridge University Press: 158, December 2002, ISBN 0-521-81496-0