查看“︁大斜方截半立方體堆砌”︁的源代码

{{NoteTA|G1=Math}}
{{Infobox polytope
| name = 大斜方截半立方體堆砌
| imagename = HC A6-A4-P2.png
| imagename2 = Cantitruncated cubic tiling.png
| caption2 = 線架圖
| polytope = 大斜方截半立方體堆砌
| Type = [[凸均勻堆砌|均勻堆砌]]
| group_type = 
| Dimension = [[三維|3]]
| dim = 
| count = 
| Cell = [[大斜方截半立方体|t<sub><small> </small></sub>{{PhysicsParticle|<big><big>{{(}}</big></big>|TR=3|BR=4}}<big><big>{{)}}</big></big>]] [[File:Great rhombicuboctahedron.png|20px]]<BR>[[截角八面體|t<sub><small> </small></sub>{3,4}]] [[File:Truncated octahedron.png|20px]]<BR>[[正方體|{4,3}]] [[File:Hexahedron.png|20px]]
| Face = [[正方形|{4}]] [[File:Kvadrato.svg|20px]]<BR>[[正六邊形|{6}]] [[File:Regular hexagon.svg|20px]]<BR>[[正八邊形|{8}]] [[File:Ośmiokąt foremny.PNG|20px]]
| Vertice_type = [[Image:Cantitruncated cubic honeycomb verf.png|50px]][[File:Omnitruncated alternated cubic honeycomb verf.png|50px]]<br>(Irreg. [[正四面體]])
| Coxeter_diagram = {{CDD|node_1|4|node_1|3|node_1|4|node}}<br>{{CDD|node_1|4|node_1|split1|nodes_11}} = {{CDD|node_1|4|node_1|3|node_1|4|node_h0}}
| Schläfli = tr{{mset|4,3,4}}<br>t<sub>0,1,2</sub>{{mset|4,3,4}}
| analogy = 
| convex = 
| Symmetry_group = <math>{\tilde{C}}_4</math>
| Space_group = Pm{{overline|3}}m (221)
| Coxeter_group =[4,3,4], <math>{\tilde{C}}_3</math>
| Fibrifold = 4<sup>−</sup>:2
| dual = triangular pyramidille
| Properties = {{link-en|顶点正|vertex-transitive}}
}}
在[[幾何學]]中，'''大斜方截半立方體堆砌'''（{{lang-en|Cantitruncated cubic honeycomb}}）是一種[[歐式幾何|歐幾里得]][[三維空間]]的半正堆砌，是由[[大斜方截半立方體]]、[[截角八面體]]和[[正方體]]以1:1:3的比例堆砌而成。

[[約翰·何頓·康威|康威]]稱'''大斜方截半立方體堆砌'''為'''n-tCO-trille'''<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>。

大斜方截半立方體堆砌應該解釋為「大斜方截角，立方體堆砌」，即對[[立方體堆砌]]進行高維度之大斜方操作（Cantitruncated）而成之[[幾何體]]

== 頂點結構 ==
四個胞周圍的每個頂點的形式為：
:[[File:2-Kuboktaederstumpf 1-Oktaederstumpf 1-Hexaeder.png|320px]]
每個頂點皆由2個[[大斜方截半立方体]]、1個[[截角八面體]]以及1個[[正方體]]所組成。

== 對稱性與表面塗色 ==
該[[幾何體]]存在兩種不同對稱性的表面塗色。線性考克斯特圖的形式可以得出同一種表面塗色每個胞的類型。分岔圖的形式，可以得出兩種類型的[[大斜方截半立方体]]有序的胞（顏色）交替。
{| class="wikitable" width=320
!結構
!大斜方截角立方
!大斜方截半交錯立方
|- valign=top
![[考克斯特标记|考克斯特群]]
![4,3,4], <math>{\tilde{C}}_3</math><br>=<[4,3<sup>1,1</sup>]>
![4,3<sup>1,1</sup>], <math>{\tilde{B}}_3</math>
|-
![[空間群]]||Pm{{overline|3}}m (221)||Fm{{overline|3}}m (225)
|-
![[Fibrifold]]||4<sup>−</sup>:2||2<sup>−</sup>:2
|- align=center
!表面塗色
|[[Image:Cantitruncated Cubic Honeycomb.svg|80px]]
|[[Image:Cantitruncated Cubic Honeycomb2.svg|80px]]
|-
![[考克斯特标记]]
!{{CDD|node_1|4|node_1|3|node_1|4|node}}
!{{CDD|node_1|4|node_1|split1|nodes_11}}
|-
![[頂點圖]]
|[[Image:Cantitruncated cubic honeycomb verf.png|80px]]
|[[File:Omnitruncated alternated cubic honeycomb verf.png|80px]]
|- align=center
!頂點<br>值<br>對稱群
|[ ]<br>order 2
|[ ]<sup>+</sup><br>order 1
|}

== 參見 ==
*[[大斜方截角立方體堆砌]]

== 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.
<references/>
[[Category:多胞体]]
[[Category:堆砌 (幾何)]]