# 大星形十二面體

(按這裡觀看旋轉模型)

3 | 2 5/2

12
30

12{5/2}

 (5/2)3（頂點圖） 大二十面體(對偶多面體)

## 性質

### 二面角

${\displaystyle \cos ^{-1}({\frac {\sqrt {5}}{5}})\approx 1.1071\approx 63.4349^{\circ }}$

### 頂點坐標

${\displaystyle (\pm {\frac {1}{2}},0,\pm {\frac {3-{\sqrt {5}}}{4}})}$
${\displaystyle (0,\pm {\frac {3-{\sqrt {5}}}{4}},\pm {\frac {1}{2}})}$
${\displaystyle (\pm {\frac {3-{\sqrt {5}}}{4}},\pm {\frac {1}{2}},0)}$
${\displaystyle (\pm {\frac {{\sqrt {5}}-1}{4}},\pm {\frac {{\sqrt {5}}-1}{4}},\pm {\frac {{\sqrt {5}}-1}{4}})}$

## 相關多面體

### 對偶複合體

 從三角形的星狀圖 從五邊形的星狀圖

## 參考文獻

1. Cauchy, A. L. "Recherches sur les polyèdres." J. de l'École Polytechnique 9, 68-86, 1813.
1. ^ Coxeter, Star polytopes and the Schläfli function f(α,β,γ) p. 121 1. The Kepler–Poinsot polyhedra
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6. ^ Johannes Kepler, Harmonices Mundi (1619).
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12. ^ Data of Great Stellated Dodecahedron. dmccooey.com. [2016-10-01]. （原始内容存档于2016-10-01）.
13. ^ Alexander Bogomolny. Great Stellated Dodecahedron. cut-the-knot.org. [2016-09-02]. （原始内容存档于2016-08-26）.
14. ^ compound of great stellated dodecahedron and great icosahedron. bulatov.org. [2016-09-02]. （原始内容存档于2015-09-06）.
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16. ^ H. Cundy and A. Rollett Great Icosahedron Plus Great Stellated Dodecahedron. §3.10.4 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 132-133, 1989.
17. ^ . Polyhedron Models. Cambridge University Press. 1974. ISBN 0-521-09859-9.
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