查看“︁交替截角八面體堆砌”︁的源代码

{{NoteTA|G1=Math}}
{{Infobox polytope
| name = 交替截角八面體堆砌
| imagename = Alternated bitruncated cubic honeycomb.png
| polytope = 交替截角八面體堆砌
| Type = [[凸均勻堆砌|均勻堆砌]]
| group_type = 
| Dimension = [[三維|3]]
| dim = 
| count = 
| Cell = [[二十面體|(3.3.3.3.3)]] [[File:Uniform polyhedron-43-h01.svg|20px]]<br>[[鍥形體|(3.3.3)]] [[File:Tetrahedron.png|20px]]
| Face = [[三角形|{3}]] [[File:Alchemical fire symbol (fixed width).svg|20px]]<br>[[等腰三角形|{3}]] [[File:Triangle.Isosceles.svg|20px]]
| Vertice_type = [[File:Alternated bitruncated cubic honeycomb verf.png|80px]]
| Coxeter_diagram = {{CDD|node|4|node_h|3|node_h|4|node}}<br>{{CDD|node|4|node_h|split1|nodes_hh}} = {{CDD|node|4|node_h|3|node_h|4|node_h0}}<br>{{CDD|node_h|split1|nodes_hh|split2|node_h}} = {{CDD|node_h0|4|node_h|3|node_h|4|node_h0}}
| Schläfli = 2s{{mset|4,3,4}}
| analogy =
| convex = 
| Symmetry_group = <math>{\tilde{C}}_3</math>, [4,3,4]
| Space_group = [[立方晶系|Im{{overline|3}}m (229)]]
| Coxeter_group = [4,3,4], <math>{\tilde{C}}_3</math>
| Coxeter_notation = [4[3<sup>[4]</sup>]]<br>↔ [<span></span>[4,3,4]]
| Fibrifold = 8<sup>o</sup>:2
| dual = 
| Properties = {{link-en|顶点正|vertex-transitive}}
}}
在[[幾何學]]中，'''交替截角八面體堆砌'''或'''交錯截角八面體堆砌'''又稱為'''雙扭稜立方體堆砌'''<ref>[[John Horton Conway|John H. Conway]], Heidi Burgiel, Chaim Goodman-Strauss, (2008) ''The Symmetries of Things'', ISBN 978-1-56881-220-5 (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, Architectonic and Catoptric tessellations, p 292-298, includes all the nonprismatic forms)</ref>是[[三維空間]]內28個半正密鋪之一，由截角八面體堆砌交替截去截角八面體胞的頂點產生擬正二十面體，剩餘空隙使用楔形四面體填滿而成。

交替截角八面體堆砌有三個相關的考克斯特圖結構：{{CDD|node|4|node_h|3|node_h|4|node}}、{{CDD|node|4|node_h|split1|nodes_hh}}和{{CDD|node_h|split1|nodes_hh|split2|node_h}}，他們分別存在[4,3<sup>+</sup>,4]、[4,(3<sup>1,1</sup>)<sup>+</sup>]與[3<sup>[4]</sup>]<sup>+</sup>的對稱性，第一個<nowiki>[[</nowiki>4,3<sup>+</sup>,4]]和最後一個[</span>[3<sup>[4]</sup>]]<sup>+</sup>的對稱性可以增加一倍。

== 表面塗色 ==
交替截角八面體堆砌有五種不同的表面塗色，其布局與截角八面體堆砌的五種表面塗色相似。下表列出各表面塗色的性質：
{| class="wikitable"
|+ 五種半正表面塗色
|-
![[空間群]]||I{{overline|3}} (204) ||Pm{{overline|3}} (200) ||Fm{{overline|3}} (202)||Fd{{overline|3}} (203) || F23 (196)
|-
![[纖維流形]]||8<sup>−o</sup>||4<sup>−</sup>||2<sup>−</sup>||2<sup>o+</sup> ||1<sup>o</sup>
|-
![[考克斯特群]]|| <nowiki>[[</nowiki>4,3<sup>+</sup>,4]]|| [4,3<sup>+</sup>,4]|| [4,(3<sup>1,1</sup>)<sup>+</sup>]|| [</span>[3<sup>[4]</sup>]]<sup>+</sup>||[3<sup>[4]</sup>]<sup>+</sup>
|- align=center
!{{link-en|考克斯特符號|Coxeter diagram}}
|{{CDD||branch_hh|4a4b|nodes}}
|{{CDD||node|4|node_h|3|node_h|4|node}}
|{{CDD|node|4|node_h|split1|nodes_hh}}
|{{CDD|branch_hh|3ab|branch_hh}}
|{{CDD|node_h|split1|nodes_hh|split2|node_h}}
|- align=center
!階
|二
|全
|半
|四分之一<BR>二
|四分之一
|-
!圖像<br>表面依胞<br>上色
|[[Image:Alternated bitruncated cubic honeycomb1.png|100px]]
|[[Image:Alternated bitruncated cubic honeycomb2.png|100px]]
|[[Image:Alternated bitruncated cubic honeycomb3.png|100px]]
|[[Image:Alternated bitruncated cubic honeycomb1.png|100px]]
|[[Image:Alternated bitruncated cubic honeycomb4.png|100px]]
|}

== 自然界中的交替截角八面體堆砌 ==
:[[File:Alfaboron.jpg|200px]]
交替截角八面體堆砌是一些分子的晶體結構，例如：α-菱形面體晶系，屬於此種晶體結構的有α-菱形硼{{sfn|Nelmes|Loveday|Allan|Besson|1993}}，交替截角八面體堆砌可以代表其中的硼原子。

交替截角八面體也可以表示面心立方晶格。二十面體的中心位於面心立方晶格的位置。<ref>Williams, 1979, p 199, Figure 5-38.</ref>

== 参考文獻 ==
* George Olshevsky, ''Uniform Panoploid Tetracombs'', Manuscript (2006) ''（包含11个凸半正镶嵌、28个凸半正堆砌、和143个凸半正四维砌的全表）''
* '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication参与编辑, 1995, ISBN 978-0-471-01003-6 [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]{{Wayback|url=http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html |date=20160711140441 }}
** (22页) H.S.M.考克斯特, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 半正空间镶嵌)
* A. Andreini, ''Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative'' (On the regular and semiregular nets of polyhedra and on the corresponding correlative nets), Mem. Società Italiana della Scienze, Ser.3, 14 (1905) 75–129.
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[[Category:多胞体]]
[[Category:堆砌 (幾何)]]