查看“︁小斜方截半立方體堆砌”︁的源代码

{{NoteTA|G1=Math}}
{{Infobox polytope
| name = 小斜方截半立方體堆砌
| imagename = HC A5-A3-P2.png
| imagename2 = Cantellated cubic tiling.png
| caption2 = 線架圖
| polytope = 小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 =[[小斜方截半立方體|rr{4,3}]] [[File:Uniform polyhedron-43-t02.png|40px]]<br/>[[截半立方體|r{4,3}]] [[File:Uniform polyhedron-43-t1.svg|40px]]<br>[[正方體|{4,3}]] [[File:Uniform polyhedron-43-t0.png|40px]]
| Face = [[三角形|{3}]] [[File:Alchemical fire symbol (fixed width).svg|20px]]<BR>[[正方形|{4}]] [[File:Kvadrato.svg|20px]]
| Vertice_type = [[File:Cantellated cubic honeycomb verf.png|75px]]<br>([[Wedge (geometry)|Wedge]])
| Coxeter_diagram = {{CDD|node_1|4|node|3|node_1|4|node}}<br>{{CDD|node_1|4|node|split1|nodes_11}} = {{CDD|node_1|4|node|3|node_1|4|node_h0}}
| Schläfli = rr{{mset|4,3,4}}<br>t<sub>0,2</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 = quarter oblate octahedrille
| Properties = {{link-en|顶点正|vertex-transitive}}
}}
在[[幾何學]]中，'''小斜方截半立方體堆砌'''是一種[[歐式幾何|歐幾里得]][[三維空間]]的半正堆砌，是由[[小斜方截半立方體]]、[[截半立方體]]和[[正方體]]以1:1:3的比例堆砌而成。

[[約翰·何頓·康威|康威]]稱'''小斜方截半立方體堆砌'''為'''2-RCO-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>，因為它可以藉由對應的[[康威多面體表示法|康威多面體變換]]而構造出來。其可以視為[[立方體堆砌]]經過「小斜方截半」[[康威多面體表示法|變換]]構造而來，也可以視為由[[小斜方截半立方體]]堆砌而得，但[[小斜方截半立方體]]無法單獨堆砌，必須和其他多面體一起堆砌，而小斜方截半立方體堆砌是小斜方截半立方體、截半立方體和正方體共同堆砌而得。

== 自然界中的小斜方截半立方體堆砌 ==
小斜方截半立方體堆砌關係到[[鈣鈦礦結構]]，在該結構中，每一個原子代表小斜方截半立方體堆砌的一個胞。
[[File:Perovskite.jpg|thumb|left|200px|鈣鈦礦結構]]

== 對稱性與表面塗色 ==
小斜方截半立方體堆砌有兩種不同對稱性的表面塗色，其中第二種表面塗色為小斜方截半立方體交錯地塗色。
{| class="wikitable" width=360
|+ 胞的表面塗色
|-
!結構
!截半立方體
!交替過截角立方體
|- valign=top
![[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||Fm{{overline|3}}m
|-
!{{link-en|考克斯特符號|Coxeter diagram}}
!{{CDD|node_1|4|node|3|node_1|4|node}}
!{{CDD|node_1|4|node|split1|nodes_11}}
|- align=center
!表面塗色
|[[File:Cantellated cubic honeycomb.png|120px]]
|[[File:Cantellated cubic honeycomb2.png|120px]]
|-
![[頂點圖]]
|[[File:Cantellated cubic honeycomb verf.png|120px]]
|[[File:Runcicantellated alternate cubic honeycomb verf.png|120px]]
|- align=center
!頂點<br>值<br>對稱性
|[ ]<br>order 2
|[ ]<sup>+</sup><br>order 1
|}

== 参考文獻 ==
{{reflist|list=
* 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.
}}

[[Category:多胞体]]
[[Category:堆砌 (幾何)]]