七角反棱柱

Template:NoteTA Template:Infobox polyhedron 在幾何學中，七角反棱柱又稱為反七角柱或七角反柱是指底為七邊形的反棱柱，側面由三角形組成，若每一個面皆為正多邊形則稱為正七角反棱柱。每個七角反棱柱皆含有16個面，是一種十六面體。

正七角反棱柱是基底為正七邊形的七角反棱柱，其可視為一種半正多面體，施萊夫利符號s{2,7}表示其可以藉由七邊形二面體透過扭稜變換構造。其具有D₇對稱群，其在Template:En-link中用| 2 2 7表示。

正七角反棱柱

• 
  正七角反棱柱

當底面為正七邊形時，會具備一些特別的性質

當基底邊長為a的時候：

• 頂點數目：14
• 邊數目：28
• 面數目：16
• 對偶多面體：七方偏方面體

高：$\frac{1}{2}a\sqrt{4-\sec \frac{\pi }{14}\sec \frac{\pi }{14}}$
表面積：$\frac{7}{2}{a}^2(\cot \frac{\pi }{7}+\sqrt{3})$
體積：$\frac{7}{12}{a}^3(\cot \frac{\pi }{14}+\cot \frac{\pi }{7})\sqrt{1-\frac{1}{4}\sec \frac{\pi }{14}\sec \frac{\pi }{14}}$

相關多面體與鑲嵌

半正七邊形二面體球面多面體

Template:Link-en：[7,2], (*722)							[7,2]+, (722)
Template:CDD	Template:CDD	Template:CDD	Template:CDD	Template:CDD	Template:CDD	Template:CDD	Template:CDD
Template:AnyLink	Template:AnyLink	Template:AnyLink	2t{7,2}=t{2,7}	Template:AnyLink	Template:AnyLink	Template:AnyLink	Template:AnyLink
半正對偶
Template:CDD	Template:CDD	Template:CDD	Template:CDD	Template:CDD	Template:CDD	Template:CDD	Template:CDD
Template:AnyLink	Template:AnyLink	Template:AnyLink	V4.4.7	Template:AnyLink	V4.4.7	Template:AnyLink	V3.3.3.7

半正反棱柱系列

2	3	4	5	6	7	8	9	10	11	12	n
s{2,4} sr{2,2}	s{2,6} sr{2,3}	s{2,8} sr{2,4}	s{2,10} sr{2,5}	s{2,12} sr{2,6}	s{2,14} sr{2,7}	s{2,16} sr{2,8}	s{2,18} sr{2,9}	s{2,20} sr{2,10}	s{2,22} sr{2,11}	s{2,24} sr{2,12}	s{2,2n} sr{2,n}
Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD	Template:CDD Template:CDD
作為球面鑲嵌

參見

• 反棱柱
• 偏方面體

參考文獻

• Fowler, P. W., T. Tarnai, and Zs Gáspár. "From circle packing to covering on a sphere with antipodal constraints." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458.2025 (2002): 2275-2287.
• heptagonal antiprismTemplate:Wayback rediff.com [2014-6-22]

外部連結

• [1]Template:Wayback
• Virtual Reality PolyhedraTemplate:Wayback www.georgehart.com: The Encyclopedia of Polyhedra
  • VRML modelTemplate:Wayback
  • Conway Notation for PolyhedraTemplate:Wayback Try: "A7"