查看“︁八角柱”︁的源代码

{{NoteTA|G1=Math}}
{{Infobox polyhedron
| name = 正八角柱
| polyhedron = 正八角柱
| imagename = Octagonal prism.png
| Type = [[柱體]]<br/>[[柱狀均勻多面體]]
| Coxeter_diagram = {{CDD|node_1|2|node_1|8|node}}<br/>{{CDD|node_1|2|node_1|4|node_1}}
| Face = 10
| Edge = 24
| Vertice = 16
| Face_type = 2個[[八邊形]] <br> 8個[[正方形]]
| Vertice_type = 4.4.8
| Face_configuration = 8{4}+2{8}
| Wythoff = 2 8 &#124; 2
| Symmetry_group = [[Dihedral symmetry in three dimensions|D<sub>8h</sub>]], [8,2], (*822), order 32
| Index_references = [[Uniform polyhedron|U]]<sub>76(f)</sub>
| Rotation_group =D<sub>8</sub>, [8,2]<sup>+</sup>, (822), order 16
| Dihedral_angle = 
| Properties = [[凸集|凸]]、 [[zonohedron]] 
| 3d_image = 
| vfigimage = Octagonal prism vertfig.png
| dual_image = Octagonal bipyramid.png
| net_image = Net of octagonal prism.svg
}}
在[[幾何學]]中，'''八角柱'''是一種[[多面體]]，是[[柱體]]的一種，是指底面是[[八邊形]]的[[柱體]]，也是第六種有無限多成員的柱體集合（八角柱包含所有底面是八邊形的柱體，即是是凹八邊形）。所有八角柱都有10個面，24個邊和16個頂點<ref name="dmccooey Octagonal Prism">{{cite web | url = http://dmccooey.com/polyhedra/SimplestD8h_2.html | title = Simplest Canonical Polyhedron with D8h Symmetry: Octagonal Prism | author = David I. McCooey | access-date = 2022-09-14 | archive-date = 2022-09-14 | archive-url = https://web.archive.org/web/20220914100144/http://dmccooey.com/polyhedra/SimplestD8h_2.html | dead-url = no }}</ref>。所有八角柱都是[[十面體]]。

如果八角柱每個面都是正多邊形，則它是[[半正多面體]]。

[[小斜方截半立方体]]切去相对的两个[[正四角帐塔]]就可以得到一个八角柱。

== 性質 ==
=== 體積 ===
若一正八角柱的[[邊長]]皆為[[1]]，則八角柱的[[體積]]為：<ref name="mw">{{cite mathworld | urlname = OctagonalPrism | title = Octagonal prism | archive-url=https://web.archive.org/web/20211020133019/https://mathworld.wolfram.com/OctagonalPrism.html | archive-date=2021-10-20}}</ref>
:<math>V = 2 + 2\sqrt{2}</math>

=== 表面積 ===
若一正八角柱的邊長皆為[[1]]，則八角柱的[[表面積]]為：<ref name="mw"/>
:<math>V = 12 + 4\sqrt{2}</math>

== 對稱性 ==
{| class=wikitable width=360
|-
!圖像
|[[File:Truncated square prism.png|180px]]
|[[File:Cantic_snub_octagonal_hosohedron.png|180px]]
|- align=center
!對稱群
|D<sub>4h</sub>, [2,4], (*422)
|D<sub>4d</sub>, [2<sup>+</sup>,8], (2*4)
|- align=center
!Constructiopn
|tr{4,2} or t{4}×{}, {{CDD|node_1|2|node_1|4|node_1}}
|s<sub>2</sub>{2,8}, {{CDD|node_h|2|node_h|8|node_1}}
|}

== 三維鑲嵌和多胞體 ==
有正八角柱的三維鑲嵌: 
{| class=wikitable width=480
|- align=center
|[[截角四角柱堆砌]]<BR>{{CDD|node_1|4|node_1|4|node|2|node_1|infin|node}}
|[[大斜方截半正方體堆砌]]<BR>{{CDD|node_1|4|node_1|3|node_1|4|node_1}}
|[[小斜方截半正方體堆砌]]<BR>{{CDD|node_1|4|node_1|3|node|4|node_1}}
|- align=center
|[[File:Truncated square prismatic honeycomb.png|160px]]
|[[File:HC A6-Pr8.png|160px]]
|[[File:HC A5-A2-P2-Pr8.png|160px]]
|}

有胞是[[正八角柱]]的多胞體: 
{|class=wikitable
|- align=center
|[[大斜方截半超立方體]]<BR>{{CDD|node_1|4|node_1|3|node|3|node_1}}
|[[小斜方截半超立方體]]<BR>{{CDD|node_1|4|node_1|3|node_1|3|node_1}}
|- align=center
|[[File:4-cube t013.svg|160px]]
|[[File:4-cube t0123.svg|160px]]
|}

== 在其他領域 ==
*在光學上，八角柱的[[棱鏡]]被用於在電影放映機產生不閃爍的圖像。
*[[十三行博物館]]的主要建築物是一個斜八角柱，象徵時間久遠遺跡毀壞無法還原的歷史真相<ref>{{cite web | url = http://www.sshm.ntpc.gov.tw/html/sshm/shcomment.jsp?cparentid=68&cid=81 | title= 十三行博物館 | publisher=sshm.ntpc.gov.tw | archive-url=https://web.archive.org/web/20130718184950/http://www.sshm.ntpc.gov.tw/html/sshm/shcomment.jsp?cparentid=68&cid=81| archive-date=2013-07-18}} 八角柱建築 在最後一段</ref><ref>{{cite web | url=https://www.sshm.ntpc.gov.tw/xmdoc/cont?xsmsid=0G244537195581528633 | publisher=sshm.ntpc.gov.tw | title=十三行博物館建築特色 | date=2017-11-22 | accessdate=2022-06-06 | archive-date=2021-01-24 | archive-url=https://web.archive.org/web/20210124105659/https://www.sshm.ntpc.gov.tw/xmdoc/cont?xsmsid=0G244537195581528633 | dead-url=no }}</ref>。
{| width=200
|- align=center
|[[File:十三行博物館外觀.JPG|thumb|200px|圖中棕色建築物即斜'''八角柱'''的[[十三行博物館]]]]
|}

== 相關多面體與鑲嵌 ==
{{稜柱列表}}
{{半正柱體}}
{|class="wikitable"
|+ 大斜方截半四階多面體和鑲嵌系列： ''4.8.2n''
|-
!rowspan=2|對稱群<BR>*n42<BR>[n,4]
!colspan=2|[[球面多面體|球面鑲嵌]]
!歐氏鑲嵌
!colspan=4|緊湊型雙曲鑲嵌
!仿緊空間
!非緊空間
|- valign=top
!*242<BR>[2,4]<BR>[[Dihedral symmetry|D<sub>4h</sub>]]
!*342<BR>[3,4]<BR>[[Tetrahedral symmetry|O<sub>h</sub>]]
!*442<BR>[4,4]<BR>P4m
!*542<BR>[5,4]
!*642<BR>[6,4]
!*742<BR>[7,4]
!*842<BR>[8,4]...
!*&infin;42<BR>[&infin;,4]
!&nbsp;<BR>[i&pi;/&lambda;,4]
|- align=center valign=bottom
!大斜方截半<br>頂點
|[[File:Spherical_octagonal_prism2.png|60px]]<br>[[正八角柱|4.8.4]]
|[[Image:Uniform tiling 432-t012.png|60px]]<br>[[大斜方截半立方體|4.8.6]]
|[[Image:Uniform tiling 44-t012.png|60px]]<br>[[截角正方形鑲嵌|4.8.8]]
|[[File:H2_tiling_245-7.png|60px]]<br>[[大斜方截半四階五邊形鑲嵌|4.8.10]]
|[[File:H2_tiling_246-7.png|60px]]<br>[[大斜方截半四階六邊形鑲嵌|4.8.12]]
|[[File:H2_tiling_247-7.png|60px]]<br>[[大斜方截半四階七邊形鑲嵌|4.8.14]]
|[[File:H2_tiling_248-7.png|60px]]<br>[[大斜方截半四階八邊形鑲嵌|4.8.16]]
|[[File:H2_tiling_24i-7.png|60px]]<br>[[大斜方截半四階無限邊形鑲嵌|4.8.&infin;]]
|<br>{{AnyLink|偽多邊形#鑲嵌與密鋪|4.8.&infin;|大斜方截半四階偽多邊形鑲嵌|type=wiki}} 
|-
![[考克斯特紀號]]<BR>[[施萊夫利符號]]
!{{CDD|node_1|2|node_1|4|node_1}}<BR>tr{2,4}
!{{CDD|node_1|3|node_1|4|node_1}}<BR>tr{3,4}
!{{CDD|node_1|4|node_1|4|node_1}}<BR>tr{4,4}
!{{CDD|node_1|5|node_1|4|node_1}}<BR>tr{5,4}
!{{CDD|node_1|6|node_1|4|node_1}}<BR>tr{6,4}
!{{CDD|node_1|7|node_1|4|node_1}}<BR>tr{7,4}
!{{CDD|node_1|8|node_1|4|node_1}}<BR>tr{8,4}
!{{CDD|node_1|infin|node_1|4|node_1}}<BR>tr{&infin;,4}
!{{CDD|node_1|ultra|node_1|4|node_1}}<BR>tr{<sup>i&pi;</sup>/<sub>&lambda;</sub>,4}
|- align=center valign=bottom
!大斜方截半<br>對偶
|[[File:Hexagonale_bipiramide.png|40px]]<br>[[雙八角錐|V4.8.4]]
|[[File:Disdyakisdodecahedron.jpg|60px]]<br>[[四角化菱形十二面體|V4.8.6]]
|[[File:Tiling Dual Semiregular V4-8-8 Tetrakis Square.svg|60px]]<br>[[四角化正方形鑲嵌|V4.8.8]]
|[[File:Order-4 bisected pentagonal tiling.png|60px]]<BR>[[八角化五階正方形鑲嵌|V4.8.10]]
|[[File:Hyperbolic domains 642.png|60px]]<BR>[[八角化六階正方形鑲嵌#鑲嵌|V4.8.12]]
|[[File:Hyperbolic domains 742.png|60px]]<BR>V4.8.14
|[[File:Hyperbolic domains 842.png|60px]]<BR>V4.8.16
|[[File:H2checkers_24i.png|60px]]<BR>V4.8.&infin;
|<BR>V4.8.&infin;
|-
!考克斯特紀號
!{{CDD|node_f1|2|node_f1|4|node_f1}}
!{{CDD|node_f1|3|node_f1|4|node_f1}}
!{{CDD|node_f1|4|node_f1|4|node_f1}}
!{{CDD|node_f1|5|node_f1|4|node_f1}}
!{{CDD|node_f1|6|node_f1|4|node_f1}}
!{{CDD|node_f1|7|node_f1|4|node_f1}}
!{{CDD|node_f1|8|node_f1|4|node_f1}}
!{{CDD|node_f1|infin|node_f1|4|node_f1}}
!{{CDD|node_f1|ultra|node_f1|4|node_f1}}
|}

== 參見 ==
== 參考文獻 ==
<references/>
* {{mathworld | urlname = OctagonalPrism | title = Octagonal prism}}

== 外部連結 ==
* [https://web.archive.org/web/20070711043500/http://polyhedra.org/poly/show/25/octagonal_prism Interactive model of an Octagonal Prism]

 {{錐體與柱體}}

[[Category:柱體]]
[[Category:均勻多面體]]