# 二十四邊形

24

t{12}

${\displaystyle \approx 45.574524676351a^{2}}$

## 正二十四邊形

${\displaystyle \cot \left({\frac {\pi }{24}}\right)=\cot \left(7.5^{\circ }\right)={\sqrt {6}}+{\sqrt {3}}+{\sqrt {2}}+2\ =\left({\sqrt {2}}+1\right)\left({\sqrt {3}}+{\sqrt {2}}\right)}$

${\displaystyle A=6t^{2}\cot {\frac {\pi }{24}}={6}t^{2}(2+{\sqrt {2}}+{\sqrt {3}}+{\sqrt {6}})}$

## 相關多邊形

{24/1}={24}

{24/2}=2{12}

{24/3}=3{8}

{24/4}=4{6}

{24/5}

{24/6}=6{4}

{24/8}=8{3}

{24/9}=3{8/3}

{24/10}=2{12/5}

{24/11}

{24/12}=12{2}

t{12}={24}

t{12/11}={24/11}

t{12/5}={24/5}

### 圖

K24完全圖經常會被以正二十四邊形的圖形繪製來描述其36條連接邊。這個圖與二十三維正二十四胞體同為24個頂點和276條邊。

 二十三維正二十四胞體

## 扭歪二十四邊形

{12}#{ } {12/5}#{ } {12/7}#{ }

## 參考文獻

1. ^
2. ^
3. ^ Eves, Howard, An Introduction to the History of Mathematics 6th, Saunders College Publishing: 131, 1992, ISBN 0-03-029558-0
4. ^ 九章算術》卷第一 - 大哉言數
5. ^
6. ^ John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278)
7. ^ The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History, (1994), Metamorphoses of polygons,