# 五角化十二面體

（按這裡觀看旋轉模型）

verse-and-dimensions的wikiaBowers acronym
pakid

60
90

arccos(−80 + 95/109)

12個階5頂點
20{6}+12{5}

I, [5,3]+, (532)

 截角二十面體（對偶多面體） （展開圖）

## 性質

### 構造

${\displaystyle H_{max}={\frac {a}{2{\sqrt {1+{\frac {1}{\varphi ^{2}}}}}}}\approx 0.425\cdot a}$

${\displaystyle {\frac {a}{{\sqrt {1+{\frac {1}{\varphi ^{2}}}}}\left(3+{\frac {1}{\varphi ^{2}}}\right)}}\approx 0.251\cdot a}$

### 面的組成

${\displaystyle \cos ^{-1}\left({\frac {19}{3{\sqrt {5}}+27}}\right)\approx 55.6906^{\circ }}$

${\displaystyle \pi -2\cos ^{-1}\left({\frac {19}{3{\sqrt {5}}+27}}\right)\approx 68.6187^{\circ }}$

## 變體

${\displaystyle {\frac {1}{{\sqrt {1+{\frac {1}{\varphi ^{2}}}}}\left(3+{\frac {1}{\varphi ^{2}}}\right)}}}$

${\displaystyle {\frac {a}{2{\sqrt {1+{\frac {1}{\varphi ^{2}}}}}}}}$

${\displaystyle {\sqrt {{\tfrac {1}{5}}\left(5+2{\sqrt {5}}\right)}}}$[4]

## 參考文獻

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