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擬詹森多面體：修订间差异

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{{noteTA
{{noteTA
|1=zh:擬Johnson多面體;zh-hans:拟约翰逊多面体; zh-hant:擬詹森多面體;
|1=zh:擬Johnson多面體; zh-hans:拟约翰逊多面体; zh-hant:擬詹森多面體;
|2=zh-hans:台塔; zh-hant:帳塔;
|2=zh-hans:台塔; zh-hant:帳塔;
|3=zh-hans:丸塔; zh-hant:罩帳;
|3=zh-hans:丸塔; zh-hant:罩帳;
第6行： 第6行：
|G1=Math
|G1=Math
}}
}}
{{Geometric Shape Example
在[[幾何學]]中，'''擬詹森多面體'''是嚴格[[凸多面體]]，其面幾乎都是[[正多邊形]]，但其中有部分或全部的面不是正多邊形但很接近正多邊形。這種多面體也包含[[詹森多面體]]，即所有的面都是[[正多邊形]]，而擬詹森多面體經常會在正多邊形與非正多邊形之間有物理構造上可以忽略的微小差異<ref>{{citation|contribution=Symmetrohedra: Polyhedra from Symmetric Placement of Regular Polygons|title=Bridges: Mathematical Connections in Art, Music and Science|year=2001|url=http://www.cgl.uwaterloo.ca/~csk/papers/kaplan_hart_bridges2001.pdf|first1=Craig S.|last1=Kaplan|first2=George W.|last2=Hart|author2-link=George W. Hart|accessdate=2014-05-01|archive-date=2015-09-23|archive-url=https://web.archive.org/web/20150923202125/http://www.cgl.uwaterloo.ca/~csk/papers/kaplan_hart_bridges2001.pdf|dead-url=no}}.</ref>。近似的精確值取決於這樣一個多面體的面逼近正多邊形的程度。
|shape class=擬詹森多面體
|Tetrated_dodecahedron.svg|name=[[四階十二面體]]
|Uncompleted rectified truncated octahedron.svg|name2=[[部分截半截角八面體]]
|Pyritohedral_near-miss_johnson.png|name3=[[五邊形六邊形五角十二面七十四面體|五邊形六邊形<br/>五角十二面七十四面體]]
|Truncated_triakis_tetrahedron.png|name4=[[截角三角化四面體]]
}}
在[[幾何學]]中，'''擬詹森多面體'''是[[嚴格凸多面體]]，其[[面 (幾何)|面]]幾乎都是[[正多邊形]]，但其中有部分或全部的[[面 (幾何)|面]]不是正多邊形但很接近正多邊形。
而擬詹森多面體經常會在正多邊形與非正多邊形之間有物理構造上可以忽略的微小差異<ref>{{citation|contribution=Symmetrohedra: Polyhedra from Symmetric Placement of Regular Polygons|title=Bridges: Mathematical Connections in Art, Music and Science|year=2001|url=http://www.cgl.uwaterloo.ca/~csk/papers/kaplan_hart_bridges2001.pdf|first1=Craig S.|last1=Kaplan|first2=George W.|last2=Hart|author2-link=George W. Hart|accessdate=2014-05-01|archive-date=2015-09-23|archive-url=https://web.archive.org/web/20150923202125/http://www.cgl.uwaterloo.ca/~csk/papers/kaplan_hart_bridges2001.pdf|dead-url=no}}.</ref>。近似的精確值取決於這樣一個多面體的面逼近正多邊形的程度。


== 例子 ==
== 例子 ==
{{clear}}
{| class="wikitable sortable"
{| class="wikitable sortable"
! 名稱<br>[[康威多面體表示法]]!! 圖像!!{{link-en|頂點布局|Vertex configuration}}!! 頂點!! 邊!! 面!! F<sub>3</sub>!! F<sub>4</sub>!! F<sub>5</sub>!! F<sub>6</sub>!! F<sub>8</sub>!! F<sub>10</sub>!! F<sub>12</sub>!! {{link-en|球面對稱群列表|List of spherical symmetry groups|對稱性}}
! 名稱<br>[[康威多面體表示法]]!! 圖像!!{{link-en|頂點布局|Vertex configuration}}!! 頂點!! 邊!! 面!! F<sub>3</sub>!! F<sub>4</sub>!! F<sub>5</sub>!! F<sub>6</sub>!! F<sub>8</sub>!! F<sub>10</sub>!! F<sub>12</sub>!! {{link-en|球面對稱群列表|List of spherical symmetry groups|對稱性}}
|- align=center
|- align=center
| [[三側錐三角柱#對偶多面體|底面截角]][[雙三角錐]]<br>[https://levskaya.github.io/polyhedronisme/?recipe=C100A1t4dP3 t4dP3]||[[File:Associahedron.gif|80px]]|| 2 (5.5.5)<br>12 (4.5.5)|| 14|| 21|| 9|| || 3|| 6|||||||||| Dih<sub>3</sub><br>order 12
| [[三側錐三角柱#對偶多面體|底面截角]][[雙三角錐]]<br/>{{AnyLink|1=https://levskaya.github.io/polyhedronisme/?recipe=C100A1t4dP3|2=t4dP3|type=ext}}||[[File:Associahedron.gif|80px]]|| 2 (5.5.5)<br>12 (4.5.5)|| 14|| 21|| 9|| || 3|| 6|||||||||| Dih<sub>3</sub><br/>12階
|- align=center
|- align=center
| [[截角三角化四面體]]<br>[https://levskaya.github.io/polyhedronisme/?recipe=C100A1t6kT t6kT]
| [[截角三角化四面體]]<br>{{AnyLink|1=https://levskaya.github.io/polyhedronisme/?recipe=C100A1t6kT|2=t6kT|type=ext}}
|[[File:Truncated triakis tetrahedron.png|80px]]
|[[File:Truncated triakis tetrahedron.png|80px]]
|4 (5.5.5)<br>24 (5.5.6)
|4 (5.5.5)<br>24 (5.5.6)
第27行： 第36行：
| &nbsp;
| &nbsp;
| &nbsp;
| &nbsp;
| ''T''<sub>d</sub>, [3,3]<br>order 24
| ''T''<sub>d</sub>, [3,3]<br>24階
|- align=center
|- align=center
|[[五邊形六邊形五角十二面七十四面體]]
|[[五邊形六邊形五角十二面七十四面體]]
第42行： 第51行：
|
|
|
|
| ''T''<sub>h</sub>, [3<sup>+</sup>,4]<br>order 24
| ''T''<sub>h</sub>, [3<sup>+</sup>,4]<br>24階
|- align=center
|- align=center
| [[倒角立方體]]<br>[https://levskaya.github.io/polyhedronisme/?recipe=C100A1cC cC]
| [[倒角立方體]]<br>{{AnyLink|1=https://levskaya.github.io/polyhedronisme/?recipe=C100A1cC|2=cC|type=ext}}
|[[File:Truncated rhombic dodecahedron.png|80px]]
|[[File:Truncated rhombic dodecahedron.png|80px]]
| 24 (4.6.6)<br>8 (6.6.6)
| 24 (4.6.6)<br>8 (6.6.6)
第57行： 第66行：
| &nbsp;
| &nbsp;
| &nbsp;
| &nbsp;
| ''O''<sub>h</sub>, [4,3]<br>order 48
| ''O''<sub>h</sub>, [4,3]<br>48階
|- align=center
|- align=center
| --
| --
第72行： 第81行：
| &nbsp;
| &nbsp;
| &nbsp;
| &nbsp;
| ''D''<sub>6h</sub>, [6,2]<br>order 24
| ''D''<sub>6h</sub>, [6,2]<br>24階
|- align=center
|- align=center
| --
| --
第87行： 第96行：
| &nbsp;
| &nbsp;
| &nbsp;
| &nbsp;
| ''D''<sub>3h</sub>, [3,2]<br>order 12
| ''D''<sub>3h</sub>, [3,2]<br>12階
|- align=center
|- align=center
| [[四階十二面體]]
| [[四階十二面體]]
第102行： 第111行：
| &nbsp;
| &nbsp;
| &nbsp;
| &nbsp;
| ''T''<sub>d</sub>, [3,3]<br>order 24
| ''T''<sub>d</sub>, [3,3]<br>24階
|- align=center
|- align=center
| [[部分截半截角八面體]]
| [[部分截半截角八面體]]
第119行： 第128行：
| ''O''<sub>h</sub>, [4,3]
| ''O''<sub>h</sub>, [4,3]
|- align=center
|- align=center
| [[倒角十二面體]]<br>[https://levskaya.github.io/polyhedronisme/?recipe=C100A1cD cD]
| [[倒角十二面體]]<br>{{AnyLink|1=https://levskaya.github.io/polyhedronisme/?recipe=C100A1cD|2=cD|type=ext}}
|[[File:Truncated rhombic triacontahedron.png|80px]]
|[[File:Truncated rhombic triacontahedron.png|80px]]
| 60 (5.6.6)<br>20 (6.6.6)
| 60 (5.6.6)<br>20 (6.6.6)
第132行： 第141行：
| &nbsp;
| &nbsp;
| &nbsp;
| &nbsp;
| ''I''<sub>h</sub>, [5,3]<br>order 120
| ''I''<sub>h</sub>, [5,3]<br>120階
|- align=center
|- align=center
| [[截半截角二十面體]]<br>[https://levskaya.github.io/polyhedronisme/?recipe=C400A1atI atI]
| [[截半截角二十面體]]<br>{{AnyLink|1=https://levskaya.github.io/polyhedronisme/?recipe=C400A1atI|2=atI|type=ext}}
| [[File:Rectified truncated icosahedron.png|80px]]
| [[File:Rectified truncated icosahedron.png|80px]]
| 60 (3.5.3.6)<br>30 (3.6.3.6)
| 60 (3.5.3.6)<br>30 (3.6.3.6)
第147行： 第156行：
| &nbsp;
| &nbsp;
| &nbsp;
| &nbsp;
| ''I''<sub>h</sub>, [5,3]<br>order 120
| ''I''<sub>h</sub>, [5,3]<br>120階
|- align=center
|- align=center
| 截角截角二十面體<br>[https://levskaya.github.io/polyhedronisme/?recipe=C1000ttI ttI]
| 截角截角二十面體<br>{{AnyLink|1=https://levskaya.github.io/polyhedronisme/?recipe=C1000ttI|2=ttI|type=ext}}
| [[File:Truncated truncated icosahedron.png|80px]]
| [[File:Truncated truncated icosahedron.png|80px]]
| 120 (3.10.12)<br>60 (3.12.12)
| 120 (3.10.12)<br>60 (3.12.12)
第162行： 第171行：
| 12
| 12
| 20
| 20
| ''I''<sub>h</sub>, [5,3]<br>order 120
| ''I''<sub>h</sub>, [5,3]<br>120階
|- align=center
|- align=center
| 擴展截角二十面體<br>[https://levskaya.github.io/polyhedronisme/?recipe=C1000aatI etI]
| 擴展截角二十面體<br>{{AnyLink|1=https://levskaya.github.io/polyhedronisme/?recipe=C1000aatI|2=etI|type=ext}}
| [[File:Expanded truncated icosahedron.png|80px]]
| [[File:Expanded truncated icosahedron.png|80px]]
| 60 (3.4.5.4)<br>120 (3.4.6.4)
| 60 (3.4.5.4)<br>120 (3.4.6.4)
第177行： 第186行：
| &nbsp;
| &nbsp;
| &nbsp;
| &nbsp;
| ''I''<sub>h</sub>, [5,3]<br>order 120
| ''I''<sub>h</sub>, [5,3]<br>120階
|- align=center
|- align=center
| 扭稜截角二十面體<br>[https://levskaya.github.io/polyhedronisme/?recipe=C1000stI stI]
| 扭稜截角二十面體<br>{{AnyLink|1=https://levskaya.github.io/polyhedronisme/?recipe=C1000stI|2=stI|type=ext}}
| [[File:Snub rectified truncated icosahedron.png|80px]]
| [[File:Snub rectified truncated icosahedron.png|80px]]
| 60 (3.3.3.3.5)<br>120 (3.3.3.3.6)
| 60 (3.3.3.3.5)<br>120 (3.3.3.3.6)
第192行： 第201行：
| &nbsp;
| &nbsp;
| &nbsp;
| &nbsp;
| ''I'', [5,3]<sup>+</sup><br>order 60
| ''I'', [5,3]<sup>+</sup><br>60階
|}
|}


== 共面擬詹森多面體 ==
== 共面擬詹森多面體 ==
有些未能成為詹森多面體的候選多面體是因為其存在有兩個以上共面的面，其也可以算是全部由正多邊形組成的凸多面體，只是其凸為非嚴格凸。<ref name="Robert R Tupelo-Schneck conditional edges">{{cite web | url= http://tupelo-schneck.org/polyhedra/|title= Convex regular-faced polyhedra with conditional edges|author= Robert R Tupelo-Schneck}}</ref>這些多面體可被看做是凸的面且非常接近正多邊形。這些立體通常有無限多種，但若約定所有頂點要位於頂角處，不能位於面（共面的一組面視為同一個面）的內部，則滿足條件的立體只有78個，可以視為詹森多面體的自然推廣<ref name="Robert R Tupelo-Schneck conditional edges"/>（參見章節[[#條件邊正多邊形凸多面體|條件邊正多邊形凸多面體]]）。
有些未能成為詹森多面體的候選多面體是因為其存在有兩個以上共面的面，其也可以算是全部由正多邊形組成的凸多面體，只是其凸為非嚴格凸。<ref name="Robert R Tupelo-Schneck conditional edges">{{cite web|url= http://tupelo-schneck.org/polyhedra/|title= Convex regular-faced polyhedra with conditional edges|author= Robert R Tupelo-Schneck|access-date= 2023-01-31|archive-date= 2021-08-18|archive-url= https://web.archive.org/web/20210818142541/http://tupelo-schneck.org/polyhedra/|dead-url= no}}</ref>這些多面體可被看做是凸的面且非常接近正多邊形。這些立體通常有無限多種，但若約定所有頂點要位於頂角處，不能位於面（共面的一組面視為同一個面）的內部，則滿足條件的立體只有78個，可以視為詹森多面體的自然推廣<ref name="Robert R Tupelo-Schneck conditional edges"/>（參見[[#條件邊正多邊形凸多面體|條件邊正多邊形凸多面體]]）。


例如：
例如：
第206行： 第215行：
File:Gyroelongated triangular bipyramid.png|二側錐八面體<br/>（[[三方偏方面體]]）
File:Gyroelongated triangular bipyramid.png|二側錐八面體<br/>（[[三方偏方面體]]）
File:Augmented_octahedron.png|正三角錐反角柱
File:Augmented_octahedron.png|正三角錐反角柱
File:Triangulated monorectified tetrahedron.png|間三側錐八面體
File:Triangulated monorectified tetrahedron.png|三側錐八面體
File:TetOct2_solid2.png|[[長八面體]]
File:TetOct2_solid2.png|{{link-en|長八面體|Elongated octahedron}}
File:Triangulated_tetrahedron.png|間四側錐八面體
File:Triangulated_tetrahedron.png|四側錐八面體
File:Augmented hexagonal antiprism flat.png|[[正六角錐反角柱]]<BR>（[[正六角反棱柱]]）
File:Augmented hexagonal antiprism flat.png|[[正六角錐反角柱]]<BR>（[[正六角反棱柱]]）
File:Augmented triangular cupola.png|
File:Augmented triangular cupola.png|
第227行： 第236行：
</gallery>
</gallery>


=== 條件邊正多邊形凸多面體 ===
=== 條件邊[[正多邊形多面體|正多邊形凸多面體]] ===
{{main|條件邊正多邊形凸多面體}}
若將詹森多面體的條件放寬成允許面兩兩共面，且所有頂點都要嚴格位於頂角上，不能有邊兩兩共線的情況（若允許邊兩兩共線，則結果會有無窮多種情況），也不能夠有頂點位於共面區域內部的情況，則能夠再列出有限個有此特性的立體。條件邊（conditional edges）指的是對應棱的二面角為平角的邊。<ref name="Robert R Tupelo-Schneck conditional edges"/>在這條件下，能允許互相共面的面有正三角形與正三角形（3+3）、正三角形與正方形（3+4）、正三角形與正五邊形（3+5）、正方形和兩個位於對側的正三角形（3+4+3）、正五邊形和兩個不相鄰的正三角形（3+5+3），也就是說，這些立體除了有正多邊形面外，也會存在上述組合之形狀的面。<ref name="Robert R Tupelo-Schneck Regular-faced Polyhedra">{{cite web | url= http://tupelo-schneck.org/polyhedra/background.html |title= Regular-faced Polyhedra |author= Robert R Tupelo-Schneck}}</ref>這類立體一共有78個。<ref name="Robert R Tupelo-Schneck conditional edges"/>和詹森多面體一樣，這些立體除了一些基本立體外，都能夠用柱體、錐體和28種立體互相組合而成。<ref name="Robert R Tupelo-Schneck Regular-faced Polyhedra"/>亞歷克斯·多斯基（Alex Doskey）<ref>{{cite web |url= http://polyhedra.doskey.com/DiamondRegular/DiamondRegular.html|title= Convex Diamond-Regular Polyhedra |author=Alex Doskey}}</ref>、羅傑·考夫曼（Roger Kaufman）和史蒂夫·沃特曼（Steve Waterman）<ref>{{cite web|url= http://watermanpolyhedron.com/dsolids.html |title= Convex hulls having regular diamonds|author= Steve Waterman}}</ref>在2006年列出了大部分有此性質的立體。2008年，維克多·扎加勒（Victor Zalgaller）<ref name="article gurin2009history">{{cite journal
{{Geometric Shape Example
|title=On the history of the study of convex polyhedra with regular faces and faces composed of regular ones
|shape class=條件邊[[正多邊形凸多面體]]
|author=Gurin, AM and Zalgaller, VA
|Green_augmented_bilunabirotunda.svg|name=[[側錐雙新月雙罩帳]]|size=121
|journal=Translations of the American Mathematical Society-Series 2
|Gyroelongated_triangular_bipyramid.png|name2=二側錐八面體
|volume=228
|Augmented octahedron.png|name3=正三角錐反角柱
|pages=169
|Elongated_digonal_gyrobicupola.png|name4=[[柱化異相雙三角柱]]|size4=90
|year=2009}}</ref>和阿列克謝·維克多羅維奇·蒂莫芬科（Aleksei Victorovich Timofeenko）<ref name= "article timofeenko2009junction">{{cite journal
}}
|title=Junction of noncomposite polygons
若將[[詹森多面體]]的條件放寬成允許面兩兩共面，且所有[[頂點 (幾何)|頂點]]都要嚴格位於頂角上，不能有邊兩兩共線的情況（若允許邊兩兩共線，則結果會有無窮多種情況），也不能夠有頂點位於共面區域內部的情況，則能夠再列出有限個有此特性的立體。條件邊（{{lang|en|conditional edges}}）指的是對應棱的二面角為平角的邊。<ref name="Robert R Tupelo-Schneck conditional edges"/>在這條件下，能允許互相共面的面有正三角形與正三角形（3+3）、正三角形與正方形（3+4）、正三角形與正五邊形（3+5）、正方形和兩個位於對側的正三角形（3+4+3）、正五邊形和兩個不相鄰的正三角形（3+5+3），也就是說，這些立體除了有正多邊形面外，也會存在上述組合之形狀的面。<ref name="Robert R Tupelo-Schneck Regular-faced Polyhedra">{{cite web | url= http://tupelo-schneck.org/polyhedra/background.html | title= Regular-faced Polyhedra | author= Robert R Tupelo-Schneck | access-date= 2023-02-01 | archive-date= 2022-11-14 | archive-url= https://web.archive.org/web/20221114153406/http://tupelo-schneck.org/polyhedra/background.html | dead-url= no }}</ref>這類立體一共有78個。<ref name="Robert R Tupelo-Schneck conditional edges"/>和詹森多面體一樣，這些立體除了一些基本立體外，都能夠用柱體、錐體和28種立體互相組合而成。<ref name="Robert R Tupelo-Schneck Regular-faced Polyhedra"/>
|author=Timofeenko, Aleksei Victorovich
|journal=Algebra i Analiz
|volume=21
|number=3
|pages=165-209
|year=2009
|publisher=St. Petersburg Department of Steklov Institute of Mathematics, Russian~…}}</ref>獨立發現並列出這些立體。2010年，蒂莫芬科證明這些立體只有78種。<ref name= "article timofeenko2009junction"/><ref name="A. V. Timofeenko 2012">{{cite journal|journal=St. Petersburg Mathematical Journal|volume=23|issue=4|language=en|issn=1061-0022|date=2012-08-01|pages=779–780|doi=10.1090/S1061-0022-2012-01217-3|url=http://www.ams.org/jourcgi/jour-getitem?pii=S1061-0022-2012-01217-3|title=Corrections to “Junction of noncomposite polyhedra”|accessdate=2023-01-31|author=Timofeenko, Aleksei Victorovich}}</ref>

{| class="wikitable sortable"
!P<sub>n,k</sub><ref name= "article timofeenko2009junction"/>
!S<sub>n</sub><ref name=" article gurin2009history"/>
!名稱
!組合
!3D模型
!頂點
!邊
!面
!F<sub>3</sub>
!F<sub>4</sub>
!F<sub>5</sub>
!F<sub>6</sub>
!F<sub>8</sub>
!F<sub>10</sub>
!F<sub>3+3</sub>
!F<sub>etc</sub>
|-
|Q<sub>1</sub>
|Q<sub>1</sub>
|斜六角柱
|（基本立體）
|[[File:Generalization of the Johnson solids q1.stl|120px]]
|12 ||18 ||8 || || 2 || || 2 || || || 4 ||
|-
|Q<sub>2</sub>
|Q<sub>2</sub>
|六斜方十二面體 （hexarhombic dodecahedron）
|（基本立體）
|[[File:Generalization of the Johnson solids q2.stl|120px]]
|18 ||28 ||12 || || 4 || || 4 || || || 4 ||
|-
|Q<sub>3</sub>
|Q<sub>3</sub>
|（未命名）
|（基本立體）
|[[File:Generalization of the Johnson solids q3.stl|120px]]
|15 ||29 ||16 || 9 || 2 || 3 || || || || 2 ||
|-
|Q<sub>4</sub>
|Q<sub>4</sub>
|（未命名）
|（基本立體）
|[[File:Generalization of the Johnson solids q4.stl|120px]]
|15 ||27 ||14 || 5 || 2 || 3 || || || || 4 ||
|-
|Q<sub>5</sub>
|Q<sub>5</sub>
|（未命名）
|（基本立體）
|[[File:Generalization of the Johnson solids q5.stl|120px]]
|22 ||42 ||22 || 10 || 4 || 2 || 2 || || || 4 ||
|-
|Q<sub>6</sub>
|Q<sub>6</sub>
|（未命名）
|（基本立體）
|[[File:Generalization of the Johnson solids q6.stl|120px]]
|18 ||33 ||17 || 7 || 3 || 3 || 1 || || || 3 ||
|-
|P<sub>2,2</sub>
|S<sub>3</sub>
|[[同相雙三角柱]]
|[[三角柱]]
|[[File:Generalization of the Johnson solids p2-2.stl|120px]]
|8 ||12 ||6 || || 4 || || || || || 2 ||
|-
|P<sub>2,3</sub>
|S<sub>4</sub>
|側三角柱立方體
|[[三角柱]]+[[立方體]]
|[[File:Generalization of the Johnson solids p2-3.stl|120px]]
|10 ||15 ||7 || || 5 || || || || || || 2
|-
|P<sub>2,4</sub>
|S<sub>5</sub>
|側三角柱五角柱
|[[三角柱]]+[[五角柱]]
|[[File:Generalization of the Johnson solids p2-4.stl|120px]]
|12 ||18 ||8 || || 6 || || || || || || 2
|-
|P<sub>2,22</sub>
|S<sub>14</sub>
|側錐四角錐
|[[正四面體]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p2-22.stl|120px]]
| 6 || 9 || 5 || 2 || 1 || || || || || 2 ||
|-
|P<sub>2,25</sub>
|S<sub>17</sub>
|側錐三角台塔
|[[三角台塔]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p2-25.stl|120px]]
| 10 || 16 || 8 || 2 || 2 || || 1 || || || 3 ||
|-
|P<sub>2,29</sub>
|S<sub>22</sub>
|側錐雙新月雙罩帳
|[[雙新月雙罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p2-29.stl|120px]]
| 15 || 29 || 16 || 9 || 2 || 3 || || || || 2 ||
|-
|P<sub>2,30</sub>
|S<sub>46</sub>
|側錐五角丸塔
|[[五角丸塔]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p2-30.stl|120px]]
| 21 || 36 || 17 || 7 || || 5 || || || 1 || 4 ||
|-
|P<sub>2,31</sub>
|S<sub>24</sub>
|五角丸塔錐
|[[五角丸塔]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p2-31.stl|120px]]
| 21 || 35 || 16 || 5 || || 5 || || || 1 || 5 ||
|-
|P<sub>2,33</sub>
|S<sub>2</sub>
|側錐三角廣底球狀罩帳
|[[三角廣底球狀罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p2-33.stl|120px]]
| 19 || 38 || 21 || 12 || 3 || 2 || 1 || || || 3 ||
|-
|P<sub>2,34</sub>
|S<sub>1</sub>
|異側鄰二側錐雙新月雙罩帳
|[[雙新月雙罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p2-34.stl|120px]]
| 16 || 32 || 18 || 10 || 2 || 2 || || || || 4 ||
|-
|P<sub>2,38</sub>
|S<sub>59</sub>
|單旋側台塔截角四面體
|[[截角四面體]]+[[三角台塔]]
|[[File:Generalization of the Johnson solids p2-38.stl|120px]]
| 15 || 24 || 11 || 2 || 3 || || 3 || || || 3 ||
|-
|P<sub>2,42</sub>
|S<sub>60</sub>
|單旋側台塔截角立方體
|[[截角立方體]]+[[四角台塔]]
|[[File:Generalization of the Johnson solids p2-42.stl|120px]]
| 28 || 44 || 18 || 4 || 5 || || || 5 || || 4 ||
|-
|P<sub>2,48</sub>
|S<sub>63</sub>
|單旋側台塔截角十二面体
|[[截角十二面体]]+[[五角台塔]]
|[[File:Generalization of the Johnson solids p2-48.stl|120px]]
| 65 || 100 || 37 || 15 || 5 || 1 || || || 11 || 5 ||
|-
|P<sub>3,1</sub>
|S<sub>6</sub>
|側錐同相雙三角柱
|[[三角柱]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p3-1.stl|120px]]
| 9 || 16 || 9 || 4 || 3 || || || || || 2 ||
|-
|P<sub>3,2</sub>
|S<sub>10</sub>
|{{link-wd|Q30634714}}
|[[三角柱]]+[[立方體]]
|[[File:Generalization of the Johnson solids p3-2.stl|120px]]
| 12 || 18 || 8 || || 4 || || || || || || 4
|-
|P<sub>3,3</sub>
|S<sub>11</sub>
|柱化同相雙三角柱
|[[三角柱]]+[[立方體]]
|[[File:Generalization of the Johnson solids p3-3.stl|120px]]
| 12 || 18 || 8 || || 6 || || || || || || 2
|-
|P<sub>3,4</sub>
|S<sub>9</sub>
|對側錐側三角柱立方體
|[[三角柱]]+[[立方體]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p3-4.stl|120px]]
| 11 || 19 || 10 || 4 || 4 || || || || || || 2
|-
|P<sub>3,5</sub>
|S<sub>12</sub>
|間二側三角柱五角柱
|[[三角柱]]+[[五角柱]]
|[[File:Generalization of the Johnson solids p3-5.stl|120px]]
| 14 || 21 || 9 || || 7 || || || || || || 2
|-
|P<sub>3,6</sub>
|S<sub>13</sub>
|間側錐側三角柱五角柱
|[[三角柱]]+[[五角柱]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p3-6.stl|120px]]
| 13 || 22 || 11 || 4 || 5 || || || || || || 2
|-
|P<sub>3,22</sub>
|S<sub>40</sub>
|五角丸塔錐柱
|[[五角丸塔]]+[[十角柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-22.stl|120px]]
| 31 || 55 || 26 || 5 || 10 || 5 || || || 1 || 5 ||
|-
|P<sub>3,31</sub>
|S<sub>41</sub>
|五角丸塔錐反棱柱
|[[五角丸塔]]+[[五角反棱柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-31.stl|120px]]
| 31 || 65 || 36 || 25 || || 5 || || || 1 || 5 ||
|-
|P<sub>3,33</sub>
|S<sub>15</sub>
|側錐八面體
|[[正八面體]]+[[正四面體]]
|[[File:Generalization of the Johnson solids p3-33.stl|120px]]
| 7 || 12 || 7 || 4 || || || || || || 3 ||
|-
|P<sub>3,34</sub>
|S<sub>18</sub>
|側錐同相雙三角台塔
|[[三角台塔]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p3-34.stl|120px]]
| 13 || 25 || 14 || 6 || 5 || || || || || 3 ||
|-
|P<sub>3,35</sub>
|S<sub>20</sub>
|側錐截半立方體
|[[截半立方體]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p3-35.stl|120px]]
| 13 || 24 || 13 || 4 || 5 || || || || || 4 ||
|-
|P<sub>3,36</sub>
|S<sub>23</sub>
|對二側錐雙新月雙罩帳
|[[雙新月雙罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-36.stl|120px]]
| 16 || 32 || 18 || 10 || 2 || 2 || || || || 4 ||
|-
|P<sub>3,37</sub>
|S<sub>47</sub>
|間二側錐五角丸塔
|[[五角丸塔]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-37.stl|120px]]
| 22 || 37 || 17 || 4 || || 4 || || || 1 || 8 ||
|-
|P<sub>3,38</sub>
|S<sub>48</sub>
|罩帳側錐異相五角帳塔罩帳
|[[五角丸塔]]+[[五角台塔]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-38.stl|120px]]
| 26 || 51 || 27 || 12 || 5 || 6 || || || || 4 ||
|-
|P<sub>3,39</sub>
|S<sub>49</sub>
|罩帳側錐同相五角帳塔罩帳
|[[五角丸塔]]+[[五角台塔]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-39.stl|120px]]
| 26 || 51 || 27 || 12 || 5 || 6 || || || || 4 ||
|-
|P<sub>3,40</sub>
|S<sub>27</sub>
|側錐截半二十面体
|[[截半二十面体]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-40.stl|120px]]
| 31 || 60 || 31 || 15 || || 11 || || || || 5 ||
|-
|P<sub>3,41</sub>
|S<sub>52</sub>
|側錐同相雙五角丸塔
|{{link-wd|Q528787}}+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-41.stl|120px]]
| 31 || 61 || 32 || 17 || || 11 || || || || 4 ||
|-
|P<sub>3,42</sub>
|S<sub>25</sub>
|異相五角帳塔罩帳錐
|[[五角帳塔]]+[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-42.stl|120px]]
| 26 || 50 || 26 || 10 || 5 || 6 || || || || 5 ||
|-
|P<sub>3,43</sub>
|S<sub>26</sub>
|同相五角帳塔罩帳錐
|[[五角帳塔]]+[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-43.stl|120px]]
| 26 || 50 || 26 || 10 || 5 || 6 || || || || 5 ||
|-
|P<sub>3,44</sub>
|S<sub>28</sub>
|同相雙五角罩帳錐
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p3-44.stl|120px]]
| 31 || 60 || 31 || 15 || || 11 || || || || 5 ||
|-
|P<sub>3,48</sub>
|S<sub>61</sub>
|單旋二側台塔截角立方體
|[[截角立方體]]+[[四角台塔]]
|[[File:Generalization of the Johnson solids p3-48.stl|120px]]
| 32 || 56 || 26 || 8 || 10 || || || 4 || || 4 ||
|-
|P<sub>3,49</sub>
|S<sub>62</sub>
|雙旋二側台塔截角立方體
|[[截角立方體]]+[[四角台塔]]
|[[File:Generalization of the Johnson solids p3-49.stl|120px]]
| 32 || 52 || 22 || || 10 || || || 4 || || 8 ||
|-
|P<sub>3,51</sub>
|S<sub>66</sub>
|單旋間二側台塔截角十二面体
|[[截角十二面体]]+[[五角台塔]]
|[[File:Generalization of the Johnson solids p3-51.stl|120px]]
| 70 || 115 || 47 || 20 || 10 || 2 || || || 10 || 5 ||
|-
|P<sub>3,53</sub>
|S<sub>64</sub>
|單旋對二側台塔截角十二面体
|[[截角十二面体]]+[[五角台塔]]
|[[File:Generalization of the Johnson solids p3-53.stl|120px]]
| 70 || 115 || 47 || 20 || 10 || 2 || || || 10 || 5 ||
|-
|P<sub>3,54</sub>
|S<sub>67</sub>
|雙旋間二側台塔截角十二面体
|[[截角十二面体]]+[[五角台塔]]
|[[File:Generalization of the Johnson solids p3-54.stl|120px]]
| 70 || 110 || 42 || 10 || 10 || 2 || || || 10 || 10 ||
|-
|P<sub>3,55</sub>
|S<sub>65</sub>
|雙旋對二側台塔截角十二面体
|[[截角十二面体]]+[[五角台塔]]
|[[File:Generalization of the Johnson solids p3-55.stl|120px]]
| 70 || 110 || 42 || 10 || 10 || 2 || || || 10 || 10 ||
|-
|P<sub>4,1</sub>
|S<sub>7</sub>
|鄰二側錐同相雙三角柱
|[[三角柱]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p4-1.stl|120px]]
| 10 || 20 || 12 || 8 || 2 || || || || || 2 ||
|-
|P<sub>4,2</sub>
|S<sub>8</sub>
|對二側錐同相雙三角柱
|[[三角柱]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p4-2.stl|120px]]
| 10 || 20 || 12 || 8 || 2 || || || || || 2 ||
|-
|P<sub>4,5</sub>
|S<sub>31</sub>
|同相五角台塔丸塔柱錐
|[[五角台塔]]+[[五角丸塔]]+[[十角柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-5.stl|120px]]
| 36 || 70 || 36 || 10 || 15 || 6 || || || || 5 ||
|-
|P<sub>4,6</sub>
|S<sub>32</sub>
|異相五角台塔丸塔柱錐
|[[五角台塔]]+[[五角丸塔]]+[[十角柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-6.stl|120px]]
| 36 || 70 || 36 || 10 || 15 || 6 || || || || 5 ||
|-
|P<sub>4,7</sub>
|S<sub>33</sub>
|同相雙五角丸塔柱錐
|[[五角丸塔]]+[[十角柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-7.stl|120px]]
| 41 || 80 || 41 || 15 || 10 || 11 || || || || 5 ||
|-
|P<sub>4,8</sub>
|S<sub>34</sub>
|異相雙五角丸塔柱錐
|[[五角丸塔]]+[[十角柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-8.stl|120px]]
| 41 || 80 || 41 || 15 || 10 || 11 || || || || 5 ||
|-
|P<sub>4,9</sub>
|S<sub>37</sub>
|五角台塔丸塔反棱柱錐
|[[五角台塔]]+[[五角丸塔]]+[[十角反棱柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-9.stl|120px]]
| 36 || 80 || 46 || 30 || 5 || 6 || || || || 5 ||
|-
|P<sub>4,10</sub>
|S<sub>38</sub>
|雙五角丸塔反棱柱錐
|[[五角丸塔]]+[[十角反棱柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-10.stl|120px]]
| 41 || 90 || 51 || 35 || || 11 || || || || 5 ||
|-
|P<sub>4,11</sub>
|S<sub>16</sub>
|二側錐八面體
|[[正四面體]]+[[正八面體]]
|[[File:Generalization of the Johnson solids p4-11.stl|120px]]
| 8 || 12 || 6 || || || || || || || 6 ||
|-
|P<sub>4,12</sub>
|S<sub>19</sub>
|間二側錐同相雙三角台塔
|[[三角台塔]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p4-12.stl|120px]]
| 14 || 26 || 14 || 4 || 4 || || || || || 6 ||
|-
|P<sub>4,13</sub>
|S<sub>21</sub>
|對二側錐截半立方體
|[[截半立方體]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p4-13.stl|120px]]
| 14 || 24 || 12 || || 4 || || || || || 8 ||
|-
|P<sub>4,14</sub>
|S<sub>50</sub>
|間二側錐異相五角帳塔罩帳
|[[五角帳塔]]+[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-14.stl|120px]]
| 27 || 52 || 27 || 9 || 5 || 5 || || || || 8 ||
|-
|P<sub>4,15</sub>
|S<sub>51</sub>
|間二側錐同相五角帳塔罩帳
|[[五角帳塔]]+[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-15.stl|120px]]
| 27 || 52 || 27 || 9 || 5 || 5 || || || || 8 ||
|-
|P<sub>4,16</sub>
|S<sub>44</sub>
|間二側錐截半二十面体
|[[截半二十面体]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-16.stl|120px]]
| 32 || 60 || 30 || 10 || || 10 || || || || 10 ||
|-
|P<sub>4,17</sub>
|S<sub>53</sub>
|同側間二側錐同相雙五角罩帳
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-17.stl|120px]]
| 32 || 62 || 32 || 14 || || 10 || || || || 8 ||
|-
|P<sub>4,18</sub>
|S<sub>29</sub>
|對二側錐截半二十面体
|[[截半二十面体]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-18.stl|120px]]
| 32 || 60 || 30 || 10 || || 10 || || || || 10 ||
|-
|P<sub>4,19</sub>
|S<sub>57</sub>
|異側鄰二側錐同相雙五角罩帳
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-19.stl|120px]]
| 32 || 62 || 32 || 14 || || 10 || || || || 8 ||
|-
|P<sub>4,20</sub>
|S<sub>58</sub>
|異側對二側錐同相雙五角罩帳
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-20.stl|120px]]
| 32 || 62 || 32 || 14 || || 10 || || || || 8 ||
|-
|P<sub>4,21</sub>
|S<sub>42</sub>
|異側側錐同相雙五角罩帳錐
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-21.stl|120px]]
| 32 || 61 || 31 || 12 || || 10 || || || || 9 ||
|-
|P<sub>4,22</sub>
|S<sub>30</sub>
|同相雙五角罩帳雙錐
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p4-22.stl|120px]]
| 32 || 60 || 30 || 10 || || 10 || || || || 10 ||
|-
|P<sub>4,25</sub>
|S<sub>68</sub>
|單旋三側帳塔截角十二面體
|[[截角十二面体]]+[[五角帳塔]]
|[[File:Generalization of the Johnson solids p4-25.stl|120px]]
| 75 || 130 || 57 || 25 || 15 || 3 || || || 9 || 5 ||
|-
|P<sub>4,26</sub>
|S<sub>69</sub>
|雙旋三側帳塔截角十二面體
|[[截角十二面体]]+[[五角帳塔]]
|[[File:Generalization of the Johnson solids p4-26.stl|120px]]
| 75 || 125 || 52 || 15 || 15 || 3 || || || 9 || 10 ||
|-
|P<sub>4,27</sub>
|S<sub>70</sub>
|三旋三側帳塔截角十二面體
|[[截角十二面体]]+[[五角帳塔]]
|[[File:Generalization of the Johnson solids p4-27.stl|120px]]
| 75 || 120 || 47 || 5 || 15 || 3 || || || 9 || 15 ||
|-
|P<sub>4,30</sub>
|
|斜四角柱
|[[正四面體]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p4-30.stl|120px]]
| 8 || 12 || 6 || || 2 || || || || || 4 ||
|-
|P<sub>4,31</sub>
|
|雙重側錐四角錐 （doubled augmented square pyramid）<br/>
雙斜三角柱 （doubled oblique triangular prism）<br/>
扭斜四角柱 （twist slant square prism）
|[[正四面體]]+[[四角錐]]
|[[File:Generalization of the Johnson solids p4-31.stl|120px]]
| 8 || 14 || 8 || 4 || 2 || || || || || 2 ||
|-
|P<sub>5,1</sub>
|S<sub>35</sub>
|同相雙五角罩帳柱雙錐
|[[五角罩帳]]+[[十角柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p5-1.stl|120px]]
| 42 || 80 || 40 || 10 || 10 || 10 || || || || 10 ||
|-
|P<sub>5,2</sub>
|S<sub>36</sub>
|異相雙五角罩帳柱雙錐
|[[五角罩帳]]+[[十角柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p5-2.stl|120px]]
| 42 || 80 || 40 || 10 || 10 || 10 || || || || 10 ||
|-
|P<sub>5,3</sub>
|S<sub>39</sub>
|雙五角罩帳反棱柱雙錐
|[[五角罩帳]]+[[十角反棱柱]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p5-3.stl|120px]]
| 42 || 90 || 50 || 30 || || 10 || || || || 10 ||
|-
|P<sub>5,4</sub>
|S<sub>45</sub>
|三側錐截半二十面体
|[[截半二十面体]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p5-4.stl|120px]]
| 33 || 60 || 29 || 5 || || 9 || || || || 15 ||
|-
|P<sub>5,5</sub>
|S<sub>55</sub>
|異側連三側錐同相雙五角罩帳
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p5-5.stl|120px]]
| 33 || 63 || 32 || 11 || || 9 || || || || 12 ||
|-
|P<sub>5,6</sub>
|S<sub>56</sub>
|異側偏三側錐同相雙五角罩帳
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p5-6.stl|120px]]
| 33 || 63 || 32 || 11 || || 9 || || || || 12 ||
|-
|P<sub>5,7</sub>
|S<sub>43</sub>
|異側間二側錐同相雙五角罩帳錐
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p5-7.stl|120px]]
| 33 || 62 || 31 || 9 || || 9 || || || || 13 ||
|-
|P<sub>6,1</sub>
|S<sub>54</sub>
|四側錐同相雙五角罩帳錐
|[[五角罩帳]]+[[五角錐]]
|[[File:Generalization of the Johnson solids p6-1.stl|120px]]
| 34 || 64 || 32 || 8 || || 8 || || || || 16 ||
|}


== 參見 ==
== 參見 ==

2024年1月15日 (一) 03:12的最新版本

擬詹森多面體
部分的擬詹森多面體
四階十二面體
四階十二面體 		部分截半截角八面體
部分截半截角八面體
五邊形六邊形 五角十二面七十四面體
五邊形六邊形
五角十二面七十四面體 		截角三角化四面體
截角三角化四面體

在幾何學中，擬詹森多面體是嚴格凸多面體，其面幾乎都是正多邊形，但其中有部分或全部的面不是正多邊形但很接近正多邊形。 而擬詹森多面體經常會在正多邊形與非正多邊形之間有物理構造上可以忽略的微小差異[1]。近似的精確值取決於這樣一個多面體的面逼近正多邊形的程度。

例子

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名稱
康威多面體表示法		 圖像 頂點布局（英语：Vertex configuration） 頂點 邊 面 F3 F4 F5 F6 F8 F10 F12 對稱性（英语：List of spherical symmetry groups）
底面截角雙三角錐
t4dP3		 2 (5.5.5)
12 (4.5.5)		 14 21 9 3 6 Dih3
12階
截角三角化四面體
t6kT 		4 (5.5.5)
24 (5.5.6) 		28 42 16     12 4       Td, [3,3]
24階
五邊形六邊形五角十二面七十四面體 12 (3.5.3.6)
24 (3.3.5.6)
24 (3.3.3.3.5) 		60 132 74 56 12 6 Th, [3+,4]
24階
倒角立方體
cC 		24 (4.6.6)
8 (6.6.6) 		32 48 18   6   12       Oh, [4,3]
48階
-- 12 (5.5.6)
6 (3.5.3.5)
12 (3.3.5.5) 		30 54 26 12   12 2       D6h, [6,2]
24階
-- 6 (5.5.5)
9 (3.5.3.5)
12 (3.3.5.5) 		27 51 26 14   12         D3h, [3,2]
12階
四階十二面體 4 (5.5.5)
12 (3.5.3.5)
12 (3.3.5.5) 		28 54 28 16   12         Td, [3,3]
24階
部分截半截角八面體 24 (3.4.3.9)
24 (3.9.9) 		38 84 48 24 6           Oh, [4,3]
倒角十二面體
cD 		60 (5.6.6)
20 (6.6.6) 		80 120 42     12 30       Ih, [5,3]
120階
截半截角二十面體
atI 		60 (3.5.3.6)
30 (3.6.3.6) 		90 180 92 60   12 20       Ih, [5,3]
120階
截角截角二十面體
ttI 		120 (3.10.12)
60 (3.12.12) 		180 270 92 60         12 20 Ih, [5,3]
120階
擴展截角二十面體
etI 		60 (3.4.5.4)
120 (3.4.6.4) 		180 360 182 60 90 12 20       Ih, [5,3]
120階
扭稜截角二十面體
stI 		60 (3.3.3.3.5)
120 (3.3.3.3.6) 		180 450 272 240   12 20       I, [5,3]+
60階

共面擬詹森多面體

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有些未能成為詹森多面體的候選多面體是因為其存在有兩個以上共面的面，其也可以算是全部由正多邊形組成的凸多面體，只是其凸為非嚴格凸。[2]這些多面體可被看做是凸的面且非常接近正多邊形。這些立體通常有無限多種，但若約定所有頂點要位於頂角處，不能位於面（共面的一組面視為同一個面）的內部，則滿足條件的立體只有78個，可以視為詹森多面體的自然推廣[2]（參見條件邊正多邊形凸多面體）。

例如： 3.3...：

参见：三角面多面體 § 非嚴格凸的情況

4.4.4.4：

3.4.6.4：

  • 正六角帳塔 （退化）
    正六角帳塔
    （退化）

條件邊正多邊形凸多面體

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主条目：條件邊正多邊形凸多面體
條件邊正多邊形凸多面體
部分的條件邊正多邊形凸多面體
側錐雙新月雙罩帳
側錐雙新月雙罩帳 		二側錐八面體
二側錐八面體
正三角錐反角柱
正三角錐反角柱 		柱化異相雙三角柱
柱化異相雙三角柱

若將詹森多面體的條件放寬成允許面兩兩共面，且所有頂點都要嚴格位於頂角上，不能有邊兩兩共線的情況（若允許邊兩兩共線，則結果會有無窮多種情況），也不能夠有頂點位於共面區域內部的情況，則能夠再列出有限個有此特性的立體。條件邊（conditional edges）指的是對應棱的二面角為平角的邊。[2]在這條件下，能允許互相共面的面有正三角形與正三角形（3+3）、正三角形與正方形（3+4）、正三角形與正五邊形（3+5）、正方形和兩個位於對側的正三角形（3+4+3）、正五邊形和兩個不相鄰的正三角形（3+5+3），也就是說，這些立體除了有正多邊形面外，也會存在上述組合之形狀的面。[3]這類立體一共有78個。[2]和詹森多面體一樣，這些立體除了一些基本立體外，都能夠用柱體、錐體和28種立體互相組合而成。[3]

參見

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參考文獻

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  1. ^ Kaplan, Craig S.; Hart, George W., Symmetrohedra: Polyhedra from Symmetric Placement of Regular Polygons, Bridges: Mathematical Connections in Art, Music and Science (PDF), 2001 [2014-05-01], （原始内容存档 (PDF)于2015-09-23） .
  2. ^ 2.0 2.1 2.2 2.3 Robert R Tupelo-Schneck. Convex regular-faced polyhedra with conditional edges. [2023-01-31]. （原始内容存档于2021-08-18）. 
  3. ^ 3.0 3.1 Robert R Tupelo-Schneck. Regular-faced Polyhedra. [2023-02-01]. （原始内容存档于2022-11-14）. 
检索自“https://zh.wikipedia.org/zhwiki/w/index.php?title=擬詹森多面體&oldid=80498770”