七角柱

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Template:NoteTA Template:Infobox polyhedron幾何學中,七角柱是一種多面體,是柱體的一種,是指底面是七邊形柱體。所有七角柱都有9個,21個和14個頂點[1]。所有七角柱都是九面體

如果七角柱每個面都是正多邊形,則它是半正多面體

正七角柱

正七角柱可以視為一種半正多面體底面正七邊形,其施萊夫利符號可以用t{2,7}或{7}x{}表示,t{2,7}是指正七角柱可以藉由七面形透過截角變換構造而來,其在Template:En-link中用2 7 | 2表示[2]

正七角柱有二種兩面角,其中一個為90,即頂面(或底面)與側面的夾角,另一個是12847[3],即兩側面的夾角。

應用

正七角柱是一種比較特殊的多面體,由於他具有一個非整數有理數角度,且與正六角柱接近[4],因此在工程學上有些應用,例如正七角柱可以用在特殊汽缸的設計[5]、正七角柱的稜鏡可以用在干涉濾光器的光信號多路復用器中[6]。除此之外,正七角柱也出現在自然界中,例如碘合氮化硼化鎂Mg8[BN2]5I)的離子為正七角柱的晶體結構[7],例如伊樂藻,有91%的親本細胞為正七角柱[8]

此外,也有人設計七角柱形的魔術方塊[9],或是經過截角變換的七角柱[10][11]

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

Template:稜柱列表 Template:半正柱體

參考文獻

  1. Heptagonal Prism Template:Wayback dmccooey.com [2014-6-22]
  2. Heptagonal prisms and antiprisms Template:Wayback umanitoba.ca [2014-6-22]
  3. Template:Cite book
  4. Template:Cite mathworld
  5. Guest, Simon D., and Sergo Pellegrino. "The folding of triangulated cylinders, Part I: Geometric considerations." Journal of applied mechanics 61.4 (1994): 773-777.
  6. Ishikawa, Shigeta. "Optical multiplexer/demultiplexer using interference filters." U.S. Patent No. 4,482,994. 13 Nov. 1984.
  7. Somer, Mehmet, et al. "Mg2[BN2]Cl and Mg8[BN2]5I: Novel Magnesium Nitridoborate Halides—Syntheses, Crystal Structures, and Vibrational Spectra." Zeitschrift für anorganische und allgemeine Chemie 630.7 (2004): 1015-1021.
  8. Van Fleet, D. S. "A comparison of histochemical and anatomical characteristics of the hypodermis with the endodermis in vascular plants." American Journal of Botany (1950): 721-725.
  9. Heptagonal Prism 3x3x3 Template:Wayback twistypuzzles.com [2014-6-22]
  10. Rubik's polyhedrons Template:Wayback twistypuzzles.com [2014-06-22]
  11. Rubik's Truncated Heptagonal prism Template:Wayback twistypuzzles.com 截角正七角柱 [2014-06-22]

外部連結

Template:錐體與柱體