# 大十二面體

（點選觀看旋轉模型）

verse-and-dimensions的wikiaBowers acronym

52 | 2 5

12
30

V(5/2)5

 (55)/2[1]（頂點圖） 小星形十二面體（對偶多面體）

## 性質

### 面的組成

 大十二面體的面 同一個五邊形面以同一種顏色標示

### 二面角

${\displaystyle \cos ^{-1}{\frac {\sqrt {5}}{5}}\approx 63.434948823^{\circ }}$

### 頂點坐標

${\displaystyle (0,\,\pm 1,\,\pm {\frac {1+{\sqrt {5}}}{4}})}$
${\displaystyle (\pm 1,\,\pm {\frac {1+{\sqrt {5}}}{4}},\,0)}$
${\displaystyle (\pm {\frac {1+{\sqrt {5}}}{4}},\,0,\,\pm 1)}$

× 20

## 使用

### 在電腦科學中

• 大十二面體也可以做為協助推算的工具之一[26]

*n32
[n,3]

*532
[5,3]
*632
[6,3]
*732
[7,3]
*832
[8,3]
*932
[9,3]
*10 32
[10,3]...
*∞32
[∞,3]

[iπ/λ,3]

(52)5

(62)6

(72)7

(82)8

(92)9

(102)10

(2)
(2)

(55)∕2

(66)∕2

(77)∕2

(88)∕2

(92)9

(102)10

(偶數)(奇數)
()∕2
()∕2

## 參考文獻

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2. Weisstein, Eric W. (编). Great Dodecahedron. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
3. Wenninger, M. J. Polyhedron Models. New York: Cambridge University Press. 1989: pp. 35 and 38-40.
4. Weisstein, Eric W. (编). Dodecahedron Stellations. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
5. Richeson, D.S. Euler's Gem: The Polyhedron Formula and the Birth of Topology. Princeton University Press. 2008: 151. ISBN 9780691126777. LCCN 2008062108.[永久失效連結]
6. Hilton, P. and Pedersen, J. and Donmoyer, S. A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics. Cambridge University Press. 2010: 171 [2017-08-08]. ISBN 9781139489072. （原始内容存档于2021-03-05）.
7. ^ , Memoire sur les polygones et polyèdres. J. de l'École Polytechnique 9, pp. 16–48, 1810.
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9. ^ Wenzel Jamnitzer. Perspectiva Corporum Regularium. 1568.
10. ^ . Polyhedron Models. Cambridge University Press. 1974. ISBN 0-521-09859-9.
11. ^ Roman E. Maeder. 35: great dodecahedron. mathconsult.ch. [2017-07-25]. （原始内容存档于2021-02-14）.
12. ^ great-dodecahedron. the universeis mental. [2017-07-25]. （原始内容存档于2017-08-07）.
13. ^ Great Dodecahedron. bulatov.org. [2017-07-25]. （原始内容存档于2021-03-05）.
14. Gijs Korthals Altes. Paper Great Dodecahedron. korthalsaltes.com. [2017-07-25]. （原始内容存档于2017-06-12）.
15. ^ Eric W. Weisstein. Great Dodecahedron. 密西根州立大學. 1999-05-25 [2017-07-25]. （原始内容存档于2021-03-05）.
16. ^ Buekenhout, F. and Cohen, A.M. Diagram Geometry: Related to Classical Groups and Buildings. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. Springer Berlin Heidelberg. 2013. ISBN 9783642344534. LCCN 2013930009.[永久失效連結]
17. ^ Stellation of Regular Maps. Regular Map database, weddslist.com. [2021-07-30]. （原始内容存档于2021-08-23）.
18. ^ S4:{5,5}. Regular Map database - map details, weddslist.com. [2021-07-30].
19. ^ Coxeter, Star polytopes and the Schläfli function f(α,β,γ) p. 121 1. The Kepler–Poinsot polyhedra
20. ^ Kepler-Poinsot Solids: Great Dodecahedron. dmccooey.com. [2017-07-25]. （原始内容存档于2021-03-05）.
21. Data of Great Dodecahedron. dmccooey.com. [2017-07-25]. （原始内容存档于2021-02-14）.
22. ^ 榎宮祐. NO GAME NO LIFE 遊戲人生[12]. 巴哈母特動畫瘋. [2017-09-07] （中文）.
23. 榎宮祐. 《NO GAME NO LIFE 遊戲人生６》 聽說遊戲玩家夫妻向世界挑戰了. 2014-04-25: 第330-331頁. EAN 4710945544663.
24. Alexander's Star - Jaap's Puzzle Page. jaapsch.net. [2017-07-25]. （原始内容存档于2021-03-05）.
25. ^ THE GREAT DODECAHEDRON. transum.org. [2017-07-25]. （原始内容存档于2021-03-05）.
26. ^ Baez, John "Golay code,页面存档备份，存于互联网档案馆）" Visual Insight, December 1, 2015.
27. Holden, A. Shapes, Space, and Symmetry. New York: Dover,. 1991: p. 103.
28. ^ Weber, Matthias, Kepler's small stellated dodecahedron as a Riemann surface, Pacific J. Math., 2005, 220: 167–182 [2017-08-07], doi:10.2140/pjm.2005.220.167, （原始内容存档于2021-03-05）
29. ^ Weisstein, Eric W. (编). Truncated great dodecahedron. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
30. ^ , Unambiguous polyhedral graphs, Israel Journal of Mathematics, 1963, 1 (4): 235–238, MR 0185506, doi:10.1007/BF02759726
31. ^ , Convex Polytopes, Wiley Interscience, 1967
32. ^ John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
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35. ^ Weisstein, Eric W. (编). Great Dodecahedron-Small Stellated Dodecahedron Compound. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.

1. . Polyhedron Models. Cambridge University Press. 1974. ISBN 0-521-09859-9.
2. Coxeter, H. S. M. The Fifty-Nine Icosahedra. Springer-Verlag, New York, Berlin, Heidelberg. 1938. ISBN 0-387-90770-X.