查看“︁環帶多面體”︁的源代码

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{{NoteTA|G1=Math}}
'''環帶多面體''' （'''全對稱多面體'''）是一種每個面都相對稱、相等或與正對的（即將兩個面的中心連起可過內接球或外接球[[球心]]）[[面]]互相對稱的立體。

==環帶多面體對於空間的填充==

==由閔可夫斯基和構成環帶多面體==

==排列構成環狀多面體==

==環帶多面體的種類==
*[[截角八面體]]有6個[[正方形]][[面]]和8個[[六邊形]]面。
*[[大斜方截半立方體]]有12個正方形面、8個六面形面和6個[[八邊形]]面。
*大斜方截半二十面體有30個正方形面、20個六邊形面和12個[[十邊形]]面。

另外，某些[[卡塔蘭立體]]（[[半正多面體]]的[[對偶多面體]]）也同樣是環帶多面體：
*[[菱形十二面體]]是[[截半立方體]]的對偶多面體。
*[[菱形三十面體]]是[[截半二十面體]]的對偶多面體。

其他有[[菱形]]面的環帶多面體：
* [[菱形二十面體]]
* [[菱面體]]
* [[菱形九十面體]]

{| class="wikitable"
|-
! 名稱(環帶多面體)
! 立體圖示
! [[對稱群]]
! [[正多邊形]]面
! [[面 (幾何)|面]] 的[[傳遞集合|可遞性]]
! [[邊 (幾何)|邊]] 的[[傳遞集合|可遞性]]
! [[頂點 (幾何)|頂點]]的[[傳遞集合|可遞性]]
! [[空間填充]](space filling)
! Number of<br/>generators
|-
| [[正方體]]<BR>4.4.4
| [[File:Hexahedron.jpg|60px|Cube]]
| [[Oh群]]
| '''有'''
| '''有'''
| '''有'''
| '''有'''
| '''有'''
| 3
|-
| [[六角柱]]<BR>4.4.6
| [[File:hexagonal_prism.png|60px|Hexagonal prism]]
| D6h群
| '''有'''
| 無
| 無
| '''有'''
| '''有'''
| 4
|-
| [[稜柱]]<BR>4.4.2n<br><math>(n>3)</math>
| [[File:octagonal_prism.png|60px|2n prism]]
| Dnh群
| '''有'''
| 無
| 無
| '''有'''
| 無
| n+1
|-
| [[截角八面體]]<BR>4.6.6
| [[File:truncatedoctahedron.jpg|60px|Truncated octahedron]]
| Oh群
| '''有'''
| 無
| 無
| '''有'''
| '''有'''
| 
|-
| [[大斜方截半立方體]]<BR><BR>4.6.8
| [[File:truncatedcuboctahedron.jpg|60px|Truncated cuboctahedron]]
| Oh群
| '''有'''
| 無
| 無
| '''有'''
| 無
| 
|-
| [[大斜方截半二十面體]]<BR>4.6.10
| [[File:truncatedicosidodecahedron.jpg|60px|Truncated icosidodecahedron]]
| [[Ih群]]
| '''有'''
| 無
| 無
| '''有'''
| 無
| 
|-
| [[菱形十二面體]]<BR>V3.4.3.4
| [[File:rhombicdodecahedron.jpg|60px|Rhombic dodecahedron]]
| Oh群
| 無
| '''有'''
| '''有'''
| 無
| '''有'''
| 
|-
| [[菱形三十面體]]<BR>V3.5.3.5
| [[File:rhombictriacontahedron.svg|60px|Rhombic triacontehedron]]
| Ih群
| 無
| '''有'''
| '''有'''
| 無
| 無
| 6
|-
| [[菱形六角化十二面體]]
| [[File:Rhombo-hexagonal dodecahedron.png|60px|Rhombo-hexagonal dodecahedron]]
| D4h群
| 無
| 無
| 無
| 無
| '''有'''
| 5
|-
| [[截角菱形十二面體]]
| [[File:Truncated rhombic dodecahedron.png|60px|Truncated Rhombic dodecahedron]]
| Oh群
| 無
| 無
| 無
| 無
| 無
|
|}

==環帶多面體的分解==
雖然多面體通不常能以相同的[[體積]]分解、組合成其他[[多面體]](請參考[[希爾伯特第三問題]])。 但任兩個環帶多面體卻得以同體積被切割、重新組合成另一方。

==參考資料==
* {{cite journal
 | author = Coxeter, H. S. M
 | authorlink = Harold Scott MacDonald Coxeter
 | year = 1962
 | title = The Classification of Zonohedra by Means of Projective Diagrams
 | journal = J. Math. Pures Appl.
 | volume = 41
 | pages = 137–156}}
* {{cite journal
 | author = Eppstein, David
 | authorlink = David Eppstein
 | year = 1996
 | title = Zonohedra and zonotopes
 | journal = [[Mathematica in Education and Research]]
 | volume = 5
 | issue = 4
 | pages = 15–21
 | url = http://www.ics.uci.edu/~eppstein/junkyard/ukraine/ukraine.html
 | access-date = 2007-12-07
 | archive-date = 2021-01-04
 | archive-url = https://web.archive.org/web/20210104120359/https://www.ics.uci.edu/~eppstein/junkyard/ukraine/ukraine.html
 | dead-url = no
 }}
* {{cite book
  | author = Grünbaum, Branko
  | authorlink = Branko Grünbaum
  | title = Arrangements and Spreads
  | publisher = Number 10 in Regional Conf. Series in Mathematics, [[美國數學學會]]
  | year = 1972}}
* {{cite journal
 | author = Fedorov, E. S.
 | year = 1893
 | title = Elemente der Gestaltenlehre
 | journal = Zeitschrift für Krystallographie und Mineralogie
 | volume = 21
 | pages = 671–694}}
* {{cite journal
 | author = Shephard, G. C.
 | year = 1974
 | title = Space-filling zonotopes
 | journal = {{tsl|en|Mathematika||Mathematika}}
 | volume = 21
 | pages = 261–269}}
* {{cite journal
 | author = Taylor, Jean E.
 | year = 1992
 | title = Zonohedra and generalized zonohedra
 | journal = [[美國數學月刊]]
 | volume = 99
 | pages = 108–111
 | doi = 10.2307/2324178}}

==外部連結==
* {{mathworld | title = Zonohedron | urlname = Zonohedron}}
* {{cite web
  | author = Eppstein, David
  | authorlink = David Eppstein
  | title = The Geometry Junkyard: Zonohedra and Zonotopes
  | url = http://www.ics.uci.edu/~eppstein/junkyard/zono.html
  | access-date = 2007-12-07
  | archive-date = 2020-03-16
  | archive-url = https://web.archive.org/web/20200316185659/https://www.ics.uci.edu/~eppstein/junkyard/zono.html
  | dead-url = no
  }}
* {{cite web
  | author = Hart, George W
  | title = Virtual Polyhedra: Zonohedra
  | url = http://www.georgehart.com/virtual-polyhedra/zonohedra-info.html
  | accessdate = 2007-12-07
  | archive-date = 2005-11-18
  | archive-url = https://web.archive.org/web/20051118212258/http://georgehart.com/virtual-polyhedra/zonohedra-info.html
  | dead-url = no
  }}
* {{mathworld | title = Primary Parallelohedron | urlname = PrimaryParallelohedron}}
* {{cite web 
  | author = Bulatov, Vladimir 
  | title = Zonohedral Polyhedra Completion 
  | url = http://bulatov.org/polyhedra/completion 
  | accessdate = 2007-12-07 
  | archive-date = 2011-08-07 
  | archive-url = https://web.archive.org/web/20110807170156/http://bulatov.org/polyhedra/completion/ 
  | dead-url = yes 
  }}

[[Category:多面体]]
[[Category:環帶多面體]]