查看“︁截半立方體堆砌”︁的源代码

{{NoteTA|G1=Math}}
{{Infobox polytope
| name = 截半立方體堆砌
| imagename =  HC A3-P3.png
| imagename2 = Rectified cubic tiling.png
| caption2 = 線架圖
| polytope = 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 = [[截半立方體|r{4,3}]] [[File:Uniform polyhedron-43-t1.svg|40px]]<br>[[正八面體|{3,4}]] [[File:Uniform polyhedron-43-t2.svg|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:Rectified cubic honeycomb verf.png|80px]]<br>[[長方體]]
| Coxeter_diagram = {{CDD|node|4|node_1|3|node|4|node}}<br>{{CDD|node|4|node_1|split1|nodes}} = {{CDD|node|4|node_1|3|node|4|node_h0}}<br>{{CDD|node_1|split1|nodes|split2|node_1}} = {{CDD|node_h0|4|node_1|split1|nodes}} = {{CDD|node_h0|4|node_1|3|node|4|node_h0}}
| Schläfli = r{{mset|4,3,4}} or t<sub>1</sub>{{mset|4,3,4}}<br>r{{mset|3<sup>[4]</sup>}}
| analogy = 截半正方形鑲嵌
| convex = 
| Symmetry_group = <math>{\tilde{C}}_4</math>
| Space_group = Pm{{overline|3}}m (221)
| Coxeter_group = <math>{\tilde{C}}_3</math>, [4,3,4]
| Fibrifold = 4<sup>−</sup>:2
| dual = 雙四角錐堆砌
| Properties = {{link-en|顶点正|vertex-transitive}}
}}
在幾何學中，'''截半立方體堆砌'''是一種歐幾里得三維空間的半正堆砌，由[[截半立方體]]和[[正八面體]]堆砌而成，是三維空間內28個半正密鋪之一，其對偶多面體為雙四角錐堆砌。

[[約翰·何頓·康威|康威]]稱'''截半立方體堆砌'''為'''cuboctahedrille'''<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[[立方體堆砌]]經過「截半」[[康威多面體表示法|變換]]構造而來，也可以視為由[[截半立方體]]堆砌而得，但[[截半立方體]]無法單獨堆砌，必須和其他多面體一起堆砌，而截半立方體堆砌是由截半立方體和正八面體共同堆砌而得。

== 表面塗色 ==
{| class="wikitable"
|- valign=top
![[考克斯特标记|對稱性]]
![4,3,4]<br><math>{\tilde{C}}_3</math>
![1<sup>+</sup>,4,3,4]<br>[4,3<sup>1,1</sup>], <math>{\tilde{B}}_3</math>
![4,3,4,1<sup>+</sup>]<br>[4,3<sup>1,1</sup>], <math>{\tilde{B}}_3</math>
![1<sup>+</sup>,4,3,4,1<sup>+</sup>]<br>[3<sup>[4]</sup>], <math>{\tilde{A}}_3</math>
|-
![[空間群]]||Pm{{overline|3}}m<br>(221)||Fm{{overline|3}}m<br>(225)||Fm{{overline|3}}m<br>(225)|| F{{overline|4}}3m<br>(216)
|- align=center
|表面塗色
|[[Image:Rectified cubic honeycomb.png|80px]]
|[[Image:Rectified cubic honeycomb4.png|80px]]
|[[Image:Rectified cubic honeycomb3.png|80px]]
|[[Image:Rectified cubic honeycomb2.png|80px]]
|- align=center
!rowspan=2|{{link-en|考克斯特符號|Coxeter diagram}}
|rowspan=2|{{CDD|node|4|node_1|3|node|4|node}}
|{{CDD|node|4|node_1|3|node|4|node_h0}}
|{{CDD|node_h0|4|node_1|3|node|4|node}}
|{{CDD|node_h0|4|node_1|3|node|4|node_h0}}
|- align=center
|{{CDD|node|4|node_1|split1|nodes}}
|{{CDD|nodes_11|split2|node|4|node}}
|{{CDD|node_1|split1|nodes|split2|node_1}}
|- align=center
![[頂點圖]]
||[[Image:Rectified cubic honeycomb verf.png|80px]]
||[[File:Rectified alternate cubic honeycomb verf.png|80px]]
||[[File:Cantellated alternate cubic honeycomb verf.png|80px]]
||[[File:T02 quarter cubic honeycomb verf.png|80px]]
|- align=center
!頂點<br>值<br>對稱性
|D<sub>4h</sub><br>[4,2]<br>(*224)<br>order 16
|D<sub>2h</sub><br>[2,2]<br>(*222)<br>order 8
|C<sub>4v</sub><br>[4]<br>(*44)<br>order 8
|C<sub>2v</sub><br>[2]<br>(*22)<br>order 4
|}

== 結構 ==
截半立方體堆砌可以被切割出一個[[截半六邊形鑲嵌]]的面，從截半立方體的六邊形中心切割，創建了兩個正三角帳塔。這部分的結構均勻，可用考克斯特記號{{CDD|node_h|2x|node_h|6|node|3|node_1}}表示，符號為s<sub>3</sub>{2,6,3}。
: [[File:Runcic_snub_263_honeycomb.png|320px]]

== 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]
** (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)]]