七角柱

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正七角柱
七角柱
正七角柱
類別 柱體
9
21
頂點 14
歐拉特徵數 F=9, E=21, V=14 (χ=2)
面的種類 七邊形×2
正方形×7
面的佈局英语Face configuration 7{4}+2{7}
頂點圖 4.4.7
考克斯特符號英语Coxeter-Dynkin diagram CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 7.pngCDel node.png
CDel node 1.pngCDel 2.pngCDel node h.pngCDel 7.pngCDel node h.png
CDel node h.pngCDel 2.pngCDel node h.pngCDel 7.pngCDel node 1.png
施萊夫利符號 t{2,7} or {7}x{}
威佐夫符號英语Wythoff symbol 2 7 | 2
康威表示法 P7
對稱群 D7h, [7,2], (*722), order 28
對偶 雙七角錐
旋轉對稱群英语Point_groups_in_three_dimensions#Rotation_groups D7, [7,2]+, (722), order 14
特性 , zonohedron , 半正
Heptagonal prism vertfig.png
4.4.7
頂點圖
Heptagonal bipyramid g.png
雙七角錐
(對偶多面體)
Net of heptagonal prism.svg
(展開圖)

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

正七角柱可以視為一種半正多面體,底面為正七邊形,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,其在威佐夫符號英语Wythoff symbol中用2 7 | 2表示[2]

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[3],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[4]、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[5]。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[6],例如伊樂藻,有91%的親本細胞為正七角柱[7]

此外,也有人設計七角柱形的魔術方塊[8],或是經過截角變換的七角柱[9][10]

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[11],即兩側面的夾角。

相關多面體與鑲嵌[编辑]

半正七邊形二面體球面多面體
對稱群英语List of spherical symmetry groups[7,2], (*722) [7,2]+, (722)
CDel node 1.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node.png CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 2.pngCDel node.png CDel node.pngCDel 7.pngCDel node 1.pngCDel 2.pngCDel node.png CDel node.pngCDel 7.pngCDel node 1.pngCDel 2.pngCDel node 1.png CDel node.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 2.pngCDel node 1.png CDel node h.pngCDel 7.pngCDel node h.pngCDel 2x.pngCDel node h.png
Heptagon.svg Regular tetradecagon.svg Heptagon.svg Spherical heptagonal prism.png Spherical heptagonal hosohedron.png Spherical truncated hexagonal prism.png Spherical heptagonal antiprism.png
{7,2} t{7,2} r{7,2} 2t{7,2}=t{2,7} 2r{7,2}={2,7} rr{7,2} tr{7,2} sr{7,2}
半正對偶
CDel node f1.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node.png CDel node f1.pngCDel 7.pngCDel node f1.pngCDel 2.pngCDel node.png CDel node.pngCDel 7.pngCDel node f1.pngCDel 2.pngCDel node.png CDel node.pngCDel 7.pngCDel node f1.pngCDel 2.pngCDel node f1.png CDel node.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node f1.png CDel node f1.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node f1.png CDel node f1.pngCDel 7.pngCDel node f1.pngCDel 2.pngCDel node f1.png CDel node fh.pngCDel 7.pngCDel node fh.pngCDel 2x.pngCDel node fh.png
Spherical heptagonal hosohedron.png Spherical dodecagonal hosohedron.png Spherical heptagonal hosohedron.png Spherical hexagonal bipyramid.png Heptagon.svg Spherical heptagonal bipyramid.png Spherical dodecagonal bipyramid.png Spherical heptagonal trapezohedron.png
V72 V142 V72 V4.4.7 V27 V4.4.7 V4.4.14 V3.3.3.7
正多邊形柱體系列
對稱群英语List of spherical symmetry groups 3 4 5 6 7 8 9 10英语Decagonal prism 11英语Hendecagonal prism 12英语Dodecagonal prism
[2n,2]
[n,2]
[2n,2+]
CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node h.png
CDel node 1.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 6.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node h.pngCDel 2.pngCDel node h.png
CDel node 1.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 8.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 8.pngCDel node h.pngCDel 2.pngCDel node h.png
CDel node 1.pngCDel 9.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 10.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 10.pngCDel node h.pngCDel 2.pngCDel node h.png
CDel node 1.pngCDel 11.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 12.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 12.pngCDel node h.pngCDel 2.pngCDel node h.png
圖像 Triangular prism.png Tetragonal prism.png
Uniform polyhedron 222-t012.png
Cube rotorotational symmetry.png
Pentagonal prism.png Hexagonal prism.png
Truncated triangle prism.png
Cantic snub hexagonal hosohedron.png
Prism 7.png Octagonal prism.png
Truncated square prism.png
Cantic snub octagonal hosohedron.png
Prism 9.png Decagonal prism.png Hendecagonal prism.png Dodecagonal prism.png
球面多面體
圖像 Spherical triangular prism.png Spherical square prism.png
Spherical square prism2.png
Spherical pentagonal prism.png Spherical hexagonal prism.png
Spherical hexagonal prism2.png
Spherical heptagonal prism.png Spherical octagonal prism.png
Spherical octagonal prism2.png
Spherical decagonal prism.png
Spherical decagonal prism2.png
柱體形式半正鑲嵌系列:
球面鑲嵌 柱體 歐式鑲嵌
仿緊空間
雙曲鑲嵌
非緊空間
Henagonal hosohedron.png
t{2,1}
CDel node.pngCDel 2.pngCDel node 1.png
Spherical digonal hosohedron.PNG
t{2,2}
CDel node 1.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node 1.png
Spherical triangular prism.png
t{3,2}
CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.png
Spherical square prism.png
{4,2}
CDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.png
Spherical pentagonal prism.png
t{5,2}
CDel node 1.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node 1.png
Spherical hexagonal prism.png
t{6,2}
CDel node 1.pngCDel 6.pngCDel node.pngCDel 2.pngCDel node 1.png
Spherical heptagonal prism.png
t{7,2}
CDel node 1.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node 1.png
Spherical octagonal prism.png
t{8,2}
CDel node 1.pngCDel 8.pngCDel node.pngCDel 2.pngCDel node 1.png
...


E2 tiling 22i-6.png
t{2,∞}
CDel node 1.pngCDel infin.pngCDel node.pngCDel 2.pngCDel node 1.png
H2 tiling 22i-6.png
t{2,iπ/λ}
CDel node 1.pngCDel ultra.pngCDel node.pngCDel 2.pngCDel node 1.png

參考文獻[编辑]

  1. ^ Heptagonal Prism dmccooey.com [2014-6-22]
  2. ^ Heptagonal prisms and antiprisms umanitoba.ca [2014-6-22]
  3. ^ 埃里克·韦斯坦因. Hexagonal prism. MathWorld. 
  4. ^ Guest, Simon D., and Sergo Pellegrino. "The folding of triangulated cylinders, Part I: Geometric considerations." Journal of applied mechanics 61.4 (1994): 773-777.
  5. ^ Ishikawa, Shigeta. "Optical multiplexer/demultiplexer using interference filters." U.S. Patent No. 4,482,994. 13 Nov. 1984.
  6. ^ 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.
  7. ^ 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.
  8. ^ Heptagonal Prism 3x3x3 twistypuzzles.com [2014-6-22]
  9. ^ Rubik's polyhedrons twistypuzzles.com [2014-06-22]
  10. ^ Rubik's Truncated Heptagonal prism twistypuzzles.com 截角正七角柱 [2014-06-22]
  11. ^ Anthony Pugh. Polyhedra: A Visual Approach. University of California Press. 1976: 27. ISBN 9780520030565 (英语). 

外部連結[编辑]