# 扭棱十二面体

(点选检视旋转模型)

|- !style="background-color:#e7dcc3"|

|| ht0,1,2{5,3}

92
150

3-5: 152°55′53″ (152.93°)

 扭棱十二面体及其手性镜像 3.3.3.3.5（顶点图） 五角化六十面体(对偶多面体) (展开图)

## 性质

### 体积与表面积

${\displaystyle A=20{\sqrt {3}}+3{\sqrt {25+10{\sqrt {5}}}}\approx 55.286\,744\,958\,445\,15}$

${\displaystyle V={\frac {12\xi ^{2}(3\varphi +1)-\xi (36\varphi +7)-(53\varphi +6)}{6{\sqrt {3-\xi ^{2}}}^{3}}}\approx 37.616\,649\,962\,733\,36}$

### 二面角

${\displaystyle \arccos \left(-{\frac {2\xi ^{2}-3}{3}}\right)\approx 2.865400688\approx 164.175366^{\circ }}$

${\displaystyle \arccos \left({\frac {-{\sqrt {15\left(4\left({\frac {1}{\xi }}-\xi \right)\left(3\varphi +1\right)+\left(12\varphi +19\right)\right)}}}{15}}\right)\approx 2.66913\approx 152.9299^{\circ }}$

${\displaystyle \xi }$定义为${\displaystyle \xi ={\sqrt[{3}]{\frac {\varphi +{\sqrt {\varphi -{\frac {5}{27}}}}}{2}}}+{\sqrt[{3}]{\frac {\varphi -{\sqrt {\varphi -{\frac {5}{27}}}}}{2}}}}$

### 顶点座标

• ${\displaystyle \left(c_{2},c_{1},c_{14}\right),\left(c_{0},c_{8},c_{12}\right),\left(c_{7},c_{6},c_{11}\right)}$，且偶数加上正号
• ${\displaystyle \left(c_{3},c_{4},c_{13}\right),\left(c_{9},c_{5},c_{10}\right)}$，且奇数加上正号，左旋与右旋则为y座标相反。

## 相关多面体与镶嵌

{5,3} t0,1{5,3} t1{5,3} t0,1{3,5} {3,5} t0,2{5,3} t0,1,2{5,3} s{5,3}

V5.5.5 V3.10.10 V3.5.3.5 V5.6.6 V3.3.3.3.3 V3.4.5.4 V4.6.10 V3.3.3.3.5

n32英语Orbifold notation

232 332 432 532 632 732 832 ∞32

5阶对称性

150