查看“︁截角立方體堆砌”︁的源代码

{{NoteTA|G1=Math}}
{{Infobox polytope
| name = 截角立方體堆砌
| imagename = HC A2-P3.png
| imagename2 = Truncated cubic tiling.png
| caption2 = 線架圖
| polytope = 截角立方體堆砌
| Type = [[凸均勻堆砌|均勻堆砌]]
| group_type = 
| Dimension = [[三維|3]]
| dim = 
| count = 
| Cell =[[截角立方體|3.8.8]] [[File:Truncated hexahedron.png|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>[[正八邊形|{8}]] [[File:Ośmiokąt foremny.PNG|20px]]
| Vertice_type = [[File:Truncated cubic honeycomb verf.png|80px]]<br>Isosceles [[四角錐]]
| Coxeter_diagram = {{CDD|node_1|4|node_1|3|node|4|node}}<br>{{CDD|node_1|4|node_1|split1|nodes}} = {{CDD|node_1|4|node_1|3|node|4|node_h0}}
| Schläfli = t{{mset|4,3,4}} or t<sub>0,1</sub>{{mset|4,3,4}}
| analogy = [[截角正方形鑲嵌]]
| 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 = 六雙立方堆砌
| Properties = {{link-en|顶点正|vertex-transitive}}
}}
在幾何學中，'''截角立方體堆砌'''是一種歐幾里得三維空間的半正堆砌，由[[截角立方體]]和[[正八面體]]堆砌而成，是三維空間內28個半正密鋪之一，其對偶多面體為六雙立方堆砌。

[[約翰·何頓·康威|康威]]稱'''截半立方體堆砌'''為'''truncated cubille'''<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「截角」[[康威多面體表示法|變換]]構造而來。

== 表面塗色 ==
{| class="wikitable" width=280
!Construction
!Bicantellated alternate cubic
!Truncated cubic honeycomb
|- valign=top
![[考克斯特群]]
![4,3<sup>1,1</sup>], <math>{\tilde{B}}_3</math>
![4,3,4], <math>{\tilde{C}}_3</math><br>=<[4,3<sup>1,1</sup>]>
|-
![[空間群]]||Fm{{overline|3}}m||Pm{{overline|3}}m
|- align=center
!表面塗色
|[[Image:Truncated cubic honeycomb2.png|120px]]
|[[Image:Truncated cubic honeycomb.png|120px]]
|- align=center
!{{link-en|考克斯特符號|Coxeter diagram}}
!{{CDD|node_1|4|node_1|split1|nodes}} = {{CDD|node_1|4|node_1|3|node|4|node_h0}}
!{{CDD|node_1|4|node_1|3|node|4|node}}
|- align=center
![[頂點圖]]
|[[File:Bicantellated alternate cubic honeycomb verf.png|80px]]
|[[Image:Truncated cubic honeycomb verf.png|80px]]
|}
== 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)]]