十九面體

常見的十九面體

十八角錐

${\displaystyle V={\frac {3hs^{2}\cot {\frac {\pi }{18}}}{2}}\approx 8.50692hs^{2}}$
${\displaystyle S={\frac {9s\left({\sqrt {4h^{2}+s^{2}\cot ^{2}{\frac {\pi }{18}}}}+s\cot {\frac {\pi }{18}}\right)}{2}}\approx 4.5s\left({\sqrt {4h^{2}+32.1634s^{2}}}+5.67128s\right)}$

十七角柱

${\displaystyle V={\frac {17hs^{2}\cot {\frac {\pi }{17}}}{4}}\approx 22.7355hs^{2}}$
${\displaystyle S=17s\left(h+{\frac {s\cot {\frac {\pi }{17}}}{2}}\right)\approx 17s\left(h+2.67476s\right)}$

十九面體列表

{17}x{}

34 51 19 2 2個十七邊形
17個矩形
D17h, [17,2], (*17 2 2), order 68

18個三角形
C18v, [18], (*18 18)

9個正方形
1個九邊形
C9v, [9], (*99)

9個梯形
9個三角形
C9v, [9], (*99)

17個梯形
D17h, [17,2], (*17 2 2), order 68

18個三角形
C6v, [6], (*66)

12個三角形
6個矩形
1個12邊形

C6v, [6], (*66)

3個梯形

13個正方形
2個十四邊形
C2v

9個正方形
2個十一邊形
C2v

參見

• 十九邊形：同為含19個維面（facet）的形狀，但是位於二維空間。

參考文獻

1. ^ Murray S. Klamkin. Problems in Applied Mathematics. SIAM. 1990. ISBN 9781611971729.
2. ^ Algonquin College, Carleton-Ottawa Mathematics Association. Crux Mathematicorum. 第 6 卷. Algonquin College. 1980: 29.
3. ^ University of Calgary. Dept. of Mathematics, Statistics, and Computing Science. Research Paper. 第 101-110 期. 1980: 22.
4. ^ Raj Chandra Bose, University of North Carolina (1793-1962). Dept. of Statistics, United States. Air Force. Office of Scientific Research. Proceedings. University of North Carolina. 1970: 232.
5. ^ George S. Innis. Existence of Binary Sequences with Prescribed Properties 11 (4): 621–622. doi:10.1137/1011101.
6. ^ Michael Goldberg, R. K. Guy, and R. K. Guy. Stability oF Polyhedra. Problem 66-12 11 (1): 621–622. 1969年1月. doi:10.1137/1011014.
7. ^ KING, R. Bruce. Supraicosahedral polyhedra in carboranes and metallacarboranes: The role of local vertex environments in determining polyhedral topology and the anomaly of 13-vertex closo polyhedra. Journal of organometallic chemistry, 2007, 692.9: 1773-1782.
8. ^ Counting polyhedra. numericana.com. [2016-01-10]. （原始内容存档于2016-05-06）.
9. Wolfram, Stephen. "Octadecagonal pyramid". from Wolfram Alpha: Computational Knowledge Engine, Wolfram Research （英语）.
10. ^ Wolfram, Stephen. "heptadecagonal prism". from Wolfram Alpha: Computational Knowledge Engine, Wolfram Research （英语）.
11. ^ Kaplan, Craig S.; Hart, George W., Symmetrohedra: Polyhedra from Symmetric Placement of Regular Polygons, Bridges: Mathematical Connections in Art, Music and Science (PDF), 2001 [2016-10-16], （原始内容存档 (PDF)于2015-09-23）.
12. ^ Aspace-filling polyhedron with 13 faces. science.unitn.it. 2016-01-10 [2016-08-28]. （原始内容存档于2017-07-01）.