查看“︁六階四面體堆砌”︁的源代码

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{{Infobox polytope
| name = 六階四面體堆砌
| imagename = H3 336 CC center.png
| polytope = 六階四面體堆砌
| Type = [[正圖形列表|雙曲正堆砌]]
| group_type = [[堆砌 (幾何)|堆砌]]
| Dimension = [[三維]][[雙曲幾何|雙曲]][[空間]]
| Cell = [[正四面體|{{mset|3,3}}]] [[File:Uniform polyhedron-33-t0.png|40px]]
| Face = [[正三角形]] {{mset|3}}
| Vertice_type = [[正三角形鑲嵌]] {{mset|3,6}}<BR>[[File:Uniform tiling 63-t2-red.svg|80px]] [[File:Uniform tiling 333-t1.svg|80px]]<BR>{{CDD|node_1|3|node|6|node}}
| Schläfli = {{mset|3,3,6}}<BR>{{mset|3,3<sup>[3]</sup>}}
| Coxeter_diagram = {{CDD|node_1|3|node|3|node|6|node}}<BR>{{CDD|node_1|3|node|3|node|6|node_h0}} ↔ {{CDD|node_1|3|node|split1|branch}}
| Symmetry_group = <math>{\bar{V}}_3</math>, [6,3,3]<BR><math>{\bar{P}}_3</math>, [3,3<sup>[3]</sup>]
| dual = [[三階六邊形鑲嵌蜂巢體]]
| Properties = [[正圖形|正]]
}}
在幾何學中，'''六階四面體堆砌'''是一種由四面體完全填滿仿緊雙曲空間的幾何結構，所謂仿緊雙曲空間是滿足[[仿紧空间]]特性的指雙曲空間，仿緊空間是指所有[[开覆盖]]都可以找到局部有限的開精細化之空間。六階四面體堆砌具有所有胞全等、所有面全等、所有邊等長、所有角等角的特性，因此是一種[[正圖形]]<ref>[[H.S.M. Coxeter|Coxeter]], ''[[Regular Polytopes (book)|Regular Polytopes]]'', 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp.&nbsp;294–296)</ref>。六階四面體堆砌的每條稜都是6個四面體的公共稜，其所有頂點都是無窮遠點，每個頂點都是無窮多個四面體的公共頂點，為正三角形鑲嵌的{{link-en|頂點排佈|Vertex_arrangement}}。其對偶幾何圖形為三階六邊形鑲嵌蜂巢體<ref>Coxeter ''The Beauty of Geometry: Twelve Essays'' (1999), Dover Publications, {{LCCN|99035678}}, ISBN 0-486-40919-8 (Chapter 10, [http://www.mathunion.org/ICM/ICM1954.3/Main/icm1954.3.0155.0169.ocr.pdf Regular Honeycombs in Hyperbolic Space] {{Wayback|url=http://www.mathunion.org/ICM/ICM1954.3/Main/icm1954.3.0155.0169.ocr.pdf |date=20160610043106 }}) Table III</ref>。

== 相關多胞體及堆砌 ==
其與二維空間中的無限接三角形鑲嵌類似，頂點都是無窮遠點
:[[File:H2checkers iii.png|120px]]
六階四面體堆砌是十一種三維仿緊正雙曲密鋪之一，其他十種三維仿緊正雙曲密鋪為：
{| class="wikitable"
!colspan=12|十一種三維仿緊正雙曲密鋪
|- align=center
|[[File:H3 633 FC boundary.png|80px]]<br/>[[三階六邊形鑲嵌蜂巢體|{6,3,3}]]<br/>（鑲嵌蜂巢體）
|[[File:H3 634 FC boundary.png|80px]]<br/>{{link-en|四階六邊形鑲嵌蜂巢體|Order-4 hexagonal tiling honeycomb|&#123;6,3,4&#125;}}<br/>（鑲嵌蜂巢體）
|[[File:H3 635 FC boundary.png|80px]]<br/>{{link-en|五階六邊形鑲嵌蜂巢體|Order-5 hexagonal tiling honeycomb|&#123;6,3,5&#125;}}<br/>（鑲嵌蜂巢體）
|[[File:H3 636 FC boundary.png|80px]]<br/>{{link-en|六階六邊形鑲嵌蜂巢體|order-6 hexagonal tiling honeycomb|&#123;6,3,6&#125;}}<br/>（鑲嵌蜂巢體）
|[[File:H3_443_FC_boundary.png|80px]]<br/>{{link-en|三階正方形鑲嵌蜂巢體|Square tiling honeycomb|&#123;4,4,3&#125;}}<br/>（鑲嵌蜂巢體）
|[[File:H3 444 FC boundary.png|80px]]<br/>{{link-en|四階正方形鑲嵌蜂巢體|Order-4_square_tiling_honeycomb|&#123;4,4,4&#125;}}<br/>（鑲嵌蜂巢體）
|- align=center
|[[File:H3 336 CC center.png|80px]]<br/>&#123;3,3,6&#125;<br/>（多面體[[堆砌 (幾何)|堆砌]]）
|[[File:H3 436 CC center.png|80px]]<br/>{{link-en|六階立方體堆砌|order-6 cubic honeycomb|&#123;4,3,6&#125;}}<br/>（多面體堆砌）
|[[File:H3_536_CC_center.png|80px]]<br/>{{link-en|六階十二面體堆砌|Order-6 dodecahedral honeycomb|&#123;5,3,6&#125;}}<br/>（多面體堆砌）
|[[File:H3_363_FC_boundary.png|80px]]<br/>{{link-en|三階三角形鑲嵌蜂巢體|Triangular tiling honeycomb|&#123;3,6,3&#125;}}<br/>（鑲嵌蜂巢體）
|[[File:H3_344_CC_center.png|80px]]<br/>{{link-en|四階八邊形鑲嵌蜂巢體|Order-4 octahedral honeycomb|&#123;3,4,4&#125;}}<br/>（鑲嵌蜂巢體）
|}

== 參見 ==
*[[七階四面體堆砌]]

== 參考文獻 ==
{{refbegin|2}}
# [[Jeffrey Weeks (mathematician)|Jeffrey R. Weeks]] ''The Shape of Space, 2nd edition'' ISBN 0-8247-0709-5 (Chapter 16-17: Geometries on Three-manifolds I,II)
# [[Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript
#* [[Norman Johnson (mathematician)|N.W. Johnson]]: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. Dissertation, University of Toronto, 1966 
#* N.W. Johnson: ''Geometries and Transformations'', (2015) Chapter 13: Hyperbolic Coxeter groups
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[[Category:堆砌 (幾何)]]