# 菱形三十面體

（按這裡觀看旋轉模型）

verse-and-dimensions的wikiaBowers acronym
rhote

30
60

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

、等面、等邊、環帶

 截半二十面体（對偶多面體） （展開圖）

## 性質

### 尺寸

${\displaystyle {\frac {25\left(5+2{\sqrt {5}}\right)}{16}}\approx 14.8}$

${\displaystyle a={\frac {\sqrt {10\left(5+{\sqrt {5}}\right)}}{8}}\approx 1.0633}$

${\displaystyle V=4{\sqrt {5+2{\sqrt {5}}}}a^{3}\approx 12.3107a^{3}}$
${\displaystyle A=12{\sqrt {5}}a^{2}\approx 26.8328a^{2}}$

${\displaystyle r_{\mathrm {m} }=\left(1+{\frac {1}{\sqrt {5}}}\right)\,a\approx 1.44721a}$
${\displaystyle r_{\mathrm {i} }={\frac {\varphi ^{2}}{\sqrt {1+\varphi ^{2}}}}\,a={\sqrt {1+{\frac {2}{\sqrt {5}}}}}\,a\approx 1.37638a}$

10 10

## 正交投影

投影對稱性 投影位置 圖像 對偶圖像 [2] [2] [6] [10] 以面為中心 以邊為中心 度為3的頂點 度為5的頂點

## 菱形三十面體圖

5 (12個)

60

### 性質

 以類似的方式呈現的菱形三十面體圖 菱形三十面體圖的另一種表示法
• 菱形三十面體圖的特徵多項式[30]
${\displaystyle x^{8}(x^{2}-15)(x^{2}-3)^{5}(x^{4}-10x^{2}+5)^{3}}$

## 參考文獻

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