查看“︁偽大斜方截半立方體”︁的源代码

{{NoteTA
|G1=Math
|1=zh:鷂形;zh-cn:筝形;zh-hk:鳶形;zh-tw:鳶形;
}}
{{Infobox polyhedron
| name = 偽大斜方截半立方體
| polyhedron = 偽大斜方截半立方體
| en_name = pseudo great rhombicuboctahedron<br/>elongated crossed square gyrobicupola
| imagename = Pseudo-great_rhombicuboctahedron.png
| Type = {{link-en|偽均勻多面體|Pseudo-uniform polyhedron|偽均勻}}[[星形多面體]]
| Face = 26
| Edge = 48
| Vertice = 24
| Face_type = 8個[[正三角形]]<br/>(8+8+2)個[[正方形]]
| Vertice_type = 4.4.4.3/2
| Vertice_configuration = 
| Schläfli = 
| Wythoff = 
| Face_configuration = 
| Conway = 
| Symmetry_group = [[二面體群|D<sub>4d</sub>]]
| Index_references = 
| Bowers_acronym = gyquerco
| dual = 偽大鳶形二十四面體
| Rotation_group = 
| Dihedral_angle = 
| Properties = 
| 3d_image = 
| vfigimage = Uniform_great_rhombicuboctahedron_vertfig.png
| dual_image = Pseudo-great_strombic_icositetrahedron.png
| net_image = 
}}
'''偽大斜方截半立方體'''是一種{{link-en|偽均勻多面體|Pseudo-uniform polyhedron}}，由8個[[正三角形]]和18個[[正方形]]組成，其[[頂點圖]]與[[非凸大斜方截半立方體]]（[[均勻多面體]]）相同，但不是均勻多面體（不滿足[[等角圖形|點可遞]]的特性），並且具有較小的對稱群，由瓊斯（Jones, R Hughes）於1994年發現並描述<ref name="article jones1994pseudo">{{cite journal
  |title = The pseudo-great rhombicuboctahedron
  |author=Jones, R Hughes
  |journal=Mathematical Scientist
  |volume=19
  |number=1
  |pages=60-63
  |year=1994
  |publisher=Canberra City, CSIRO, Division of Mathematics and Statistics
 }}</ref><ref name="article webb2003stella">{{cite journal
  |title=Stella: polyhedron navigator
  |author=Webb, Robert
  |journal=Symmetry: Culture and Science
  |volume=11
  |number=1-4
  |pages=231-268
  |year=2003}}</ref><ref name="book bezdek2003discrete">{{cite book
  |title=Discrete Geometry
  |author=Bezdek, A.
  |isbn=9780824747619
  |series=Chapman & Hall/CRC Pure and Applied Mathematics
  |url=https://books.google.com.tw/books?id=PJLrmnOR98AC
  |year=2003
  |publisher=Taylor & Francis
  }}</ref>{{rp|362}}。其可以藉由將[[非凸大斜方截半立方體]]的局部旋轉45[[度 (角)|度]]構成，這種特性就類似[[小斜方截半立方体]]與[[異相雙四角台塔柱]]的關係。<ref name="An enduring error"/>

== 性質 ==
偽大斜方截半立方體由26個[[面 (幾何)|面]]、48條[[邊 (幾何)|邊]]和24個[[頂點 (幾何)|頂點]]組成。在其26個面中，有8個三角形和18個正方形，在18個正方形中，可以分成3組，一組是在[[非凸大斜方截半立方體]]變換成偽大斜方截半立方體旋轉的部件上，各4個，共八個；另一組為非凸大斜方截半立方體變換成偽大斜方截半立方體不動的8個正方形（作為八角星柱的側面）；<ref name="An enduring error">{{cite journal
 | last = Grünbaum | first = Branko
 | doi = 10.4171/EM/120
 | issue = 3
 | journal = Elemente der Mathematik
 | mr = 2520469
 | pages = 89–101
 | title = An enduring error
 | volume = 64
 | year = 2009| doi-access = free
}}</ref>以及剩餘的2個正方形。

=== 頂角的組成 ===
在偽大斜方截半立方體的24個頂點中，每個頂點都是3個正方形和1個三角形的公共頂點<ref>{{cite web | url = http://www.georgehart.com/virtual-polyhedra/pseudo-rhombicuboctahedra.html | title = Pseudo Rhombicuboctahedra | author = George W. Hart | access-date = 2022-08-20 | archive-date = 2012-12-08 | archive-url = https://web.archive.org/web/20121208043333/http://www.georgehart.com/virtual-polyhedra/pseudo-rhombicuboctahedra.html | dead-url = no }}</ref>，並且這些面在構成頂角的多面角時，以三角形、正方形、正方形和正方形的順序排列，在[[頂點圖]]中可以用{{nowrap|(3.4.4.4)}}來表示<ref name="An enduring error"/>，更精確地，若要表達三角形反向相接的特性，有時會將3改成{{nowrap|3/2}}<ref name="software3d.com">{{cite web | url = https://www.software3d.com/Pseudo.php | title = Pseudo Great Rhombicuboctahedron | website = software3d.com | author = Robert Webb | access-date = 2022-08-20 | archive-date = 2022-08-20 | archive-url = https://web.archive.org/web/20220820140807/https://www.software3d.com/Pseudo.php | dead-url = no }}</ref>，即{{nowrap|3/2.4.4.4}}。
{| class=wikitable width=200px
|[[File:Uniform_great_rhombicuboctahedron_vertfig.png|200px]]<br/>將偽大斜方截半立方體的頂角視覺化的圖形
|}

=== 構造 ===
偽大斜方截半立方體可以從[[非凸大斜方截半立方體]]構造而成，其方法為從[[非凸大斜方截半立方體]]中取一個正方形面和8個與該正方形共用頂點的面（取下來的形狀類似無八角星底面的{{link-en|交叉四角帳塔|Crossed_square_cupola}}）並將這個取下的部件旋轉45[[度 (角)|度]]（<math>\frac{\pi}{4}</math>）即可構成偽大斜方截半立方體。<ref name="An enduring error"/>
{| class=wikitable width=600px
|[[File:Uniform great rhombicuboctahedron.png|150px]]<br/>[[非凸大斜方截半立方體]]
|[[File:Crossed_square_cupola.png|150px]]<br/>要從[[非凸大斜方截半立方體]]旋轉的部分形似{{link-en|交叉四角帳塔|Crossed_square_cupola}}
|[[File:Prism 8-3 without octagram.png|150px]]<br/>不變的部分形似{{link-en|八角星柱|Octagrammic prism}}
|[[File:Pseudo-great_rhombicuboctahedron.png|150px]]<br/>變換完的形狀，即偽大斜方截半立方體
|}

== 相關多面體 ==
偽大斜方截半立方體也稱為異相雙交叉四角台塔柱（elongated crossed square gyrobicupola）類似於[[異相雙四角台塔柱]]的名稱。
{| class="wikitable" width=350px
|- valign=top
|[[Image:Uniform great rhombicuboctahedron.png|150px]]<br>[[非凸大斜方截半立方體]]
|[[File:Pseudo-great rhombicuboctahedron.png|150px]]<br>偽大斜方截半立方體
|}

== 參見 ==
*[[非凸大斜方截半立方體]]

== 參考文獻 ==
{{Reflist}}

[[Category:星形多面体]]
[[Category:非凸多面體]]