# 截半二十面体

(按這裡觀看旋轉模型)

verse-and-dimensions的wikiaBowers acronym
id

r{5,3}
t1{5,3}

2 | 3 5

32
60

20個{3}
12個{5}

quasiregular

 3.5.3.5（頂點圖） 菱形三十面體（對偶多面體） （展開圖）

## 性質

### 體積與表面積

${\displaystyle A=\left(5{\sqrt {3}}+3{\sqrt {5}}{\sqrt {3+4\phi }}\right)a^{2}}$ ${\displaystyle =\left(5{\sqrt {3}}+3{\sqrt {25+10{\sqrt {5}}}}\right)a^{2}\approx 29.3059828a^{2}}$
${\displaystyle V={\frac {1}{3}}\left(14+17\phi \right)a^{3}={\frac {1}{6}}\left(45+17{\sqrt {5}}\right)a^{3}\approx 13.8355259a^{3}.}$

### 二面角

${\displaystyle \arccos {(-{\sqrt {\frac {5+2{\sqrt {5}}}{15}}})}\approx 142.62^{\circ }}$

### 頂點坐標

${\displaystyle \left(0\,,0\,,\pm \varphi \right)}$[7]
1/2, ±φ/2, ±1 + φ/2)[7]

## 相關多面體及鑲嵌

### 相關多面體

 原始形狀

{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

## 參考文獻

1. ^ Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 137, 1987. ISBN 978-0486253572
2. ^ Cundy, H. and Rollett, A. "Icosidodecahedron. (3.5)2." §3.7.8 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 108, 1989.
3. ^ Weisstein, Eric W. (编). Icosidodecahedron. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
4. ^ Archimedean Solids: Icosidodecahedron. dmccooey.com. （原始内容存档于2016-03-24）.
5. ^ The Icosidodecahedron. eusebeia. [2016-08-30]. （原始内容存档于2016-12-03）.
6. ^ Weisstein, Eric W. (编). Icosahedral group. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
7. Klitzing, Richard. icosidodecahedron: o3x5o - id. bendwavy.org. [2016-08-30]. （原始内容存档于2016-03-24）.
8. ^
9. icosidodecahedron:Id-facetings. polyedergarten. [2016-08-30]. （原始内容存档于2017-01-11）.