# 小三角六边形二十面体

20
60

5個六邊形的公共頂點
3個六邊形的公共頂點

(對偶多面體)

## 性質

### 頂點座標

${\displaystyle (0,\pm {\frac {5-{\sqrt {5}}}{10}},\pm {\frac {5+{\sqrt {5}}}{10}})}$
${\displaystyle (\pm {\frac {5+{\sqrt {5}}}{10}},0,\pm {\frac {5-{\sqrt {5}}}{10}})}$
${\displaystyle (\pm {\frac {5-{\sqrt {5}}}{10}},\pm {\frac {5+{\sqrt {5}}}{10}},0)}$
${\displaystyle (\pm {\frac {3-{\sqrt {5}}}{2}},0,\pm {\frac {{\sqrt {5}}-1}{2}})}$
${\displaystyle (\pm {\frac {{\sqrt {5}}-1}{2}},\pm {\frac {3-{\sqrt {5}}}{2}},0)}$
${\displaystyle (0,\pm {\frac {{\sqrt {5}}-1}{2}},\pm {\frac {3-{\sqrt {5}}}{2}})}$
${\displaystyle (\pm {\frac {\sqrt {5}}{5}},\pm {\frac {\sqrt {5}}{5}},\pm {\frac {\sqrt {5}}{5}})}$

### 二面角

${\displaystyle \cos ^{-1}(-{\frac {1}{3}})\approx 1.9106\approx 109.4712^{\circ }}$

### 體積與表面積

${\displaystyle A=3{\sqrt {15}}a^{2}\approx 11.61895a^{2}}$
${\displaystyle V={\frac {5+3{\sqrt {5}}}{4}}a^{3}\approx 2.92705a^{3}.}$

## 參考文獻

1. Wenninger, Magnus. Polyhedron Models. Cambridge University Press. 1974. ISBN 0-521-09859-9.
2. Wenninger, Magnus. Dual Models. Cambridge University Press. 1983. ISBN 0-521-54325-8.
3. Coxeter, Harold Scott MacDonald; Du Val, P.; Flather, H. T.; Petrie, J. F. The fifty-nine icosahedra 3rd. Tarquin. 1999. ISBN 978-1-899618-32-3. MR676126. (1st Edn University of Toronto (1938))
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