# 鳶形二十四面體

（按這裡觀看旋轉模型）

verse-and-dimensions的wikiaBowers acronym

deC

24
48

arccos(−7 + 42/17)

V3.4.4.4

O, [4,3]+, (432)

 V3.4.4.4（頂點圖） 小斜方截半立方体（對偶多面體） （展開圖）

## 性質

### 體積與表面積

{\displaystyle {\begin{aligned}A&=6{\sqrt {29-2{\sqrt {2}}}}\,a^{2}\\V&={\sqrt {122+71{\sqrt {2}}}}\,a^{3}\end{aligned}}}

### 頂點坐標

${\displaystyle \left(0\,,\quad 0\,,\quad \pm {\sqrt {2}}\right)}$
${\displaystyle \left(\pm {\sqrt {2}}\,,\quad 0\,,\quad 0\right)}$
${\displaystyle \left(0\,,\quad \pm {\sqrt {2}}\,,\quad 0\right)}$
${\displaystyle \left(\pm 1\,,\quad 0\,,\quad \pm 1\right)}$
${\displaystyle \left(\pm 1\,,\quad \pm 1\,,\quad 0\right)}$
${\displaystyle \left(0\,,\quad \pm 1\,,\quad \pm 1\right)}$
${\displaystyle \left(\pm {\frac {4+{\sqrt {2}}}{7}}\,,\quad \pm {\frac {4+{\sqrt {2}}}{7}}\,,\quad \pm {\frac {4+{\sqrt {2}}}{7}}\right)}$

## 正交投影

投影對稱性 圖像 對偶圖像 [2] [4] [6]

## 相關多面體與鑲嵌

 鳶形二十四面體 複合八面體立方體與左圖同一個角度

{4,3} t0,1{4,3} t1{4,3} t1,2{4,3} {3,4} t0,2{4,3} t0,1,2{4,3} s{4,3} h{4,3} h1,2{4,3}

V4.4.4 V3.8.8 V3.4.3.4 V4.6.6 V3.3.3.3 V3.4.4.4 V4.6.8 V3.3.3.3.4 V3.3.3 V3.3.3.3.3
*變異的n42對稱性對偶擴展鑲嵌系列：V3.4.n.4

*232
[2,3]
*332
[3,3]
*432
[4,3]
*532
[5,3]
*632
[6,3]
*732
[7,3]
*832
[8,3]...
*∞32
[∞,3]

V3.4.2.4

V3.4.3.4

V3.4.4.4

V3.4.5.4

V3.4.6.4

V3.4.8.4

V3.4.∞.4

3.4.2.4

3.4.3.4

3.4.4.4

3.4.5.4

3.4.6.4

3.4.8.4

3.4.∞.4

### 偏方二十四面體

, Oh, 24階 , Th, 12階

## 鳶形二十四面體圖

### 性質

${\displaystyle x^{8}{\left(x^{2}-14\right)}{\left(x^{2}-8\right)}^{3}{\left(x^{2}-2\right)}^{5}}$

## 參考文獻

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