# 三側錐六角柱

J56 - J57 - J58

verse-and-dimensions的wikiaBowers acronym
tauhip

17
30

3 正方形
2 六边形

12(32.4.6)

 （展開圖）

## 性質

### 体积与表面积

${\displaystyle A=(3+6{\sqrt {3}})a^{2}}$

${\displaystyle V={\frac {{\sqrt {2}}+3{\sqrt {3}}}{2}}a^{3}}$

### 頂點座標

${\displaystyle \left(\pm 1,\,\pm {\sqrt {3}},\,\pm 1\right),}$
${\displaystyle \left(\pm 2,\,0,\,\pm 1\right),}$
${\displaystyle \left(\pm {\frac {3+{\sqrt {6}}}{2}},\,{\frac {3+{\sqrt {6}}}{2{\sqrt {3}}}},\,0\right),}$
${\displaystyle \left(0,\,-{\frac {3+{\sqrt {6}}}{\sqrt {3}}},\,0\right).}$

### 二面角

${\displaystyle \angle }$正方形${\displaystyle ,}$六邊形${\displaystyle \,=90^{\circ }}$

${\displaystyle \angle }$三角形${\displaystyle ,}$正方形${\displaystyle \,=\arccos \left(-{\frac {1+{\sqrt {6}}}{\sqrt {12}}}\right)\approx 3.04971172\approx 174.73561029^{\circ }}$

${\displaystyle \angle }$三角形${\displaystyle ,}$六邊形${\displaystyle \,=\arccos \left(-{\sqrt {\frac {2}{3}}}\right)\approx 2.52611294\approx 144.73561004^{\circ }}$

${\displaystyle \angle }$三角形${\displaystyle ,}$三角形${\displaystyle \,=\arccos \left(-{\frac {1}{3}}\right)\approx 1.91063324\approx 109.47122085^{\circ }}$

## 參考文獻

1. , Convex polyhedra with regular faces, , 1966, 18: 169–200, MR 0185507, Zbl 0132.14603, doi:10.4153/cjm-1966-021-8.
2. ^ Apolinar, E.S. Illustrated Glossary for School Mathematics. 2023 [2023-01-17]. ISBN 9786072941311. （原始内容存档于2023-01-17）.
3. Apolinar, E.S. 2023[2], p.471. [2023-01-29]. （原始内容存档于2023-01-29）.
4. ^ David I. McCooey. Johnson Solids: Triaugmented Hexagonal Prism. [2023-01-17]. （原始内容存档于2023-05-21）.
5. The Triaugmented Hexagonal Prism. qfbox.info. [2023-01-17]. （原始内容存档于2023-02-08）.
6. Richard Klitzing. triaugmented hexagonal prism, tauhip. bendwavy.org. [2023-01-17]. （原始内容存档于2023-01-29）.