查看“︁詹森多面體列表”︁的源代码

{{noteTA
|1=zh:Johnson多面體;zh-hans:约翰逊多面体; zh-hant:詹森多面體;
|2=zh-hans:台塔; zh-hant:帳塔;
|3=zh-hans:丸塔; zh-hant:罩帳;
|4=zh-hans:约翰逊; zh-hant:詹森;
|G1=Math
}}
'''[[詹森多面體]]'''是指的所有[[面 (幾何)|面]]都是[[正多邊形]]但[[頂點 (幾何)|頂點]]並非均勻的[[嚴格凸多面體]]。
即不是[[柏拉圖立體|柏拉图立体]]、不是[[阿基米德立體]]、不是[[半正多面體]]、不是[[棱柱]]也不是[[反棱柱]]的[[嚴格凸多面體|嚴格凸]][[正多邊形多面體]]。
1966年，{{Le|諾曼·詹森|Norman Johnson (mathematician)}}發表了一份包含92種有以上性質的多面體列表，並給出了名稱和編號，但他並未證明這種立體僅有92個，但猜想沒有其他的這種立體。<ref>{{cite journal | last=Johnson | first=Norman W. | author-link=Norman Johnson (mathematician) | title=Convex Solids with Regular Faces | url=https://archive.org/details/sim_canadian-journal-of-mathematics_1966_18_1/page/169 | journal=Canadian Journal of Mathematics | volume=18 | year=1966 | pages=169–200 | zbl=0132.14603 | issn=0008-414X | doi=10.4153/cjm-1966-021-8| doi-access=free }}</ref>
1969年，維克多·扎加勒（Victor Zalgaller）證明了詹森多面體僅有92個，也就是諾曼·詹森給出的多面體列表是完整的。<ref>{{cite journal | last=Zalgaller | first=Victor A. | author-link=Victor Zalgaller | title=Convex Polyhedra with Regular Faces | language=ru | journal=Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova | volume=2 | pages=1–221 | year=1967 | issn=0373-2703 | zbl=0165.56302 }}</ref>

另外，也可能構造出具有近似於正多邊形面的[[凸多面體]]；或可以構造所有面都是正多邊形但不要求嚴格凸的凸多面體。這些多面體被非正式地稱為[[擬詹森多面體]]；它們的數量無法被確定，後者則有無窮多種。但後者如果加上一個「條件邊」的條件，則可以確定其數量為78個，稱為[[條件邊正多邊形凸多面體]]<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>。詳細的這些立體可以參見[[條件邊正多邊形凸多面體列表]]<ref name= "article timofeenko2009junction">{{cite journal
  |title=Junction of noncomposite polygons
  |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>。

下表列出了92種詹森多面體的各項重要性質與數值。每個表都允許按特定欄位的內容來做排序，以便依據特定屬性或性質或詹森多面體的名稱來進行排序。

== 列表 ==
下表列出詹森多面體的名稱與[[展開圖]]：
{| class="wikitable sortable" width=100%
|-
! {{math|''J''<sub>''n''</sub>}}
! 名稱
! 英語名稱
! [[展開圖]]
! 圖像
|-
| 1
| [[正四角錐]]
| Square pyramid
| [[Image:Johnson solid 1 net.png|80px]]
| [[Image:Square pyramid.png|80px]]
|-
| 2
| [[正五角錐]]
| Pentagonal pyramid
| [[Image:Johnson solid 2 net.png|80px]]
| [[Image:Pentagonal pyramid.png|80px]]
|-
| 3
| [[正三角帳塔]]
| Triangular cupola
| [[Image:Johnson solid 3 net.png|80px]]
| [[Image:Triangular cupola.png|80px]]
|-
| 4
| [[正四角帳塔]]
| Square cupola
| [[Image:Johnson solid 4 net.png|80px]]
| [[Image:Square cupola.png|80px]]
|-
| 5
| [[正五角帳塔]]
| Pentagonal cupola
| [[Image:Johnson solid 5 net.png|80px]]
| [[Image:Pentagonal cupola.png|80px]]
|-
| 6
| [[正五角罩帳]]
| Pentagonal rotunda
| [[Image:Johnson solid 6 net.png|80px]]
| [[Image:Pentagonal rotunda.png|80px]]
|-
| 7
| [[正三角錐柱]]
| Elongated triangular pyramid
| [[Image:Johnson solid 7 net.png|80px]]
| [[Image:Elongated triangular pyramid.png|80px]]
|-
| 8
| [[正四角錐柱]]
| Elongated square pyramid
| [[Image:Johnson solid 8 net.png|80px]]
| [[Image:Elongated square pyramid.png|80px]]
|-
| 9
| [[正五角錐柱]]
| Elongated pentagonal pyramid
| [[Image:Johnson solid 9 net.png|80px]]
| [[Image:Elongated pentagonal pyramid.png|80px]]
|-
| 10
| [[四角錐反角柱]]
| Gyroelongated square pyramid
| [[Image:Johnson solid 10 net.png|80px]]
| [[Image:Gyroelongated square pyramid.png|80px]]
|-
| 11
| [[五角錐反角柱]]
| Gyroelongated pentagonal pyramid
| [[Image:Johnson solid 11 net.png|80px]]
| [[Image:Gyroelongated pentagonal pyramid.png|80px]]
|-
| 12
| [[雙三角錐]]
| Triangular bipyramid
| [[Image:Johnson solid 12 net.png|80px]]
| [[Image:Triangular dipyramid.png|80px]]
|-
| 13
| [[雙五角錐]]
| Pentagonal bipyramid
| [[Image:Johnson solid 13 net.png|80px]]
| [[Image:Pentagonal dipyramid.png|80px]]
|-
| 14
| [[雙三角錐柱]]
| Elongated triangular bipyramid
| [[Image:Johnson solid 14 net.png|80px]]
| [[Image:Elongated triangular dipyramid.png|80px]]
|-
| 15
| [[雙四角錐柱]]
| Elongated square bipyramid
| [[Image:Johnson solid 15 net.png|80px]]
| [[Image:Elongated square dipyramid.png|80px]]
|-
| 16
| [[雙五角錐柱]]
| Elongated pentagonal bipyramid
| [[Image:Johnson solid 16 net.png|80px]]
| [[Image:Elongated pentagonal dipyramid.png|80px]]
|-
| 17
| [[雙四角錐反角柱]]
| Gyroelongated square bipyramid
| [[Image:Johnson solid 17 net.png|80px]]
| [[Image:Gyroelongated square dipyramid.png|80px]]
|-
| 18
| [[三角帳塔柱]]
| Elongated triangular cupola
| [[Image:Johnson solid 18 net.png|80px]]
| [[Image:Elongated triangular cupola.png|80px]]
|-
| 19
| [[四角帳塔柱]]
| Elongated square cupola
| [[Image:Johnson solid 19 net.png|80px]]
| [[Image:Elongated square cupola.png|80px]]
|-
| 20
| [[五角帳塔柱]]
| Elongated pentagonal cupola
| [[Image:Johnson solid 20 net.png|80px]]
| [[Image:Elongated pentagonal cupola.svg|80px]]
|-
| 21
| [[正五角罩帳柱]]
| Elongated pentagonal rotunda
| [[Image:Johnson solid 21 net.png|80px]]
| [[Image:Elongated pentagonal rotunda.png|80px]]
|-
| 22
| [[正三角帳塔反角柱]]
| Gyroelongated triangular cupola
| [[Image:Johnson solid 22 net.png|80px]]
| [[Image:Gyroelongated triangular cupola.png|80px]]
|-
| 23
| [[正四角帳塔反角柱]]
| Gyroelongated square cupola
| [[Image:Johnson solid 23 net.png|80px]]
| [[Image:Gyroelongated square cupola.png|80px]]
|-
| 24
| [[正五角台塔反角柱]]
| Gyroelongated pentagonal cupola
| [[Image:Johnson solid 24 net.png|80px]]
| [[Image:Gyroelongated pentagonal cupola.png|80px]]
|-
| 25
| [[正五角罩帳反角柱]]
| Gyroelongated pentagonal rotunda
| [[Image:Johnson solid 25 net.png|80px]]
| [[Image:Gyroelongated pentagonal rotunda.png|80px]]
|-
| 26
| [[異相雙三角柱]]
| Gyrobifastigium
| [[Image:Johnson solid 26 net.png|80px]]
| [[Image:Gyrobifastigium.png|80px]]
|-
| 27
| [[同相雙三角台塔]]
| Triangular orthobicupola
| [[Image:Johnson solid 27 net.png|80px]]
| [[Image:Triangular orthobicupola.png|80px]]
|-
| 28
| [[同相雙四角台塔]]
| Square orthobicupola
| [[Image:Johnson solid 28 net.png|80px]]
| [[Image:Square orthobicupola.png|80px]]
|-
| 29
| [[異相雙四角台塔]]
| Square gyrobicupola
| [[Image:Johnson solid 29 net.png|80px]]
| [[Image:Square gyrobicupola.png|80px]]
|-
| 30
| [[同相雙五角台塔]]
| Pentagonal orthobicupola
| [[Image:Johnson solid 30 net.png|80px]]
| [[Image:Pentagonal orthobicupola.png|80px]]
|-
| 31
| [[異相雙五角台塔]]
| Pentagonal gyrobicupola
| [[Image:Johnson solid 31 net.png|80px]]
| [[Image:Pentagonal gyrobicupola.png|80px]]
|-
| 32
| [[同相五角台塔丸塔]]
| Pentagonal orthocupolarotunda
| [[Image:Johnson solid 32 net.png|80px]]
| [[Image:Pentagonal orthocupolarotunda.png|80px]]
|-
| 33
| [[異相五角台塔丸塔]]
| Pentagonal gyrocupolarotunda
| [[Image:Johnson solid 33 net.png|80px]]
| [[Image:Pentagonal gyrocupolarotunda.png|80px]]
|-
| 34
| {{link-en|同相雙五角丸塔|Pentagonal orthobirotunda}}
| Pentagonal orthobirotunda
| [[Image:Johnson solid 34 net.png|80px]]
| [[Image:Pentagonal orthobirotunda.png|80px]]
|-
| 35
| {{link-en|同相雙三角台塔柱|Elongated triangular orthobicupola}}
| Elongated triangular orthobicupola
| [[Image:Johnson solid 35 net.png|80px]]
| [[Image:Elongated triangular orthobicupola.png|80px]]
|-
| 36
| {{link-en|異相雙三角台塔柱|Elongated triangular gyrobicupola}}
| Elongated triangular gyrobicupola
| [[Image:Johnson solid 36 net.png|80px]]
| [[Image:Elongated triangular gyrobicupola.png|80px]]
|-
| 37
| [[異相雙四角台塔柱]]
| Elongated square gyrobicupola
| [[Image:Johnson solid 37 net.png|80px]]
| [[Image:Elongated square gyrobicupola.png|80px]]
|-
| 38
| {{link-en|同相雙五角台塔柱|Elongated pentagonal orthobicupola}}
| Elongated pentagonal orthobicupola
| [[Image:Johnson solid 38 net.png|80px]]
| [[Image:Elongated pentagonal orthobicupola.png|80px]]
|-
| 39
| {{link-en|異相雙五角台塔柱|Elongated pentagonal gyrobicupola}}
| Elongated pentagonal gyrobicupola
| [[Image:Johnson solid 39 net.png|80px]]
| [[Image:Elongated pentagonal gyrobicupola.png|80px]]
|-
| 40
| {{link-en|同相五角台塔丸塔柱|Elongated pentagonal orthocupolarotunda}}
| Elongated pentagonal orthocupolarotunda
| [[Image:Johnson solid 40 net.png|80px]]
| [[Image:Elongated pentagonal orthocupolarotunda.png|80px]]
|-
| 41
| {{link-en|異相五角台塔丸塔柱|Elongated pentagonal gyrocupolarotunda}}
| Elongated pentagonal gyrocupolarotunda
| [[Image:Johnson solid 41 net.png|80px]]
| [[Image:Elongated pentagonal gyrocupolarotunda.png|80px]]
|-
| 42
| {{link-en|同相五角雙丸塔柱|Elongated pentagonal orthobirotunda}}
| Elongated pentagonal orthobirotunda
| [[Image:Johnson solid 42 net.png|80px]]
| [[Image:Elongated pentagonal orthobirotunda.png|80px]]
|-
| 43
| {{link-en|異相五角雙丸塔柱|Elongated pentagonal gyrobirotunda}}
| Elongated pentagonal gyrobirotunda
| [[Image:Johnson solid 43 net.png|80px]]
| [[Image:Elongated pentagonal gyrobirotunda.png|80px]]
|-
| 44
| {{link-en|雙三角台塔反角柱|Gyroelongated triangular bicupola}}
| Gyroelongated triangular bicupola
| [[Image:Johnson solid 44 net.png|80px]]
| [[Image:Gyroelongated triangular bicupola.png|80px]]
|-
| 45
| {{link-en|雙四角台塔反角柱|Gyroelongated square bicupola}}
| Gyroelongated square bicupola
| [[Image:Johnson solid 45 net.png|80px]]
| [[Image:Gyroelongated square bicupola.png|80px]]
|-
| 46
| {{link-en|雙五角台塔反角柱|Gyroelongated pentagonal bicupola}}
| Gyroelongated pentagonal bicupola
| [[Image:Johnson solid 46 net.png|80px]]
| [[Image:Gyroelongated pentagonal bicupola.png|80px]]
|-
| 47
| {{link-en|五角台塔丸塔反角柱|Gyroelongated pentagonal cupolarotunda}}
| Gyroelongated pentagonal cupolarotunda
| [[Image:Johnson solid 47 net.png|80px]]
| [[Image:Gyroelongated pentagonal cupolarotunda.png|80px]]
|-
| 48
| {{link-en|雙五角丸塔反角柱|Gyroelongated pentagonal birotunda}}
| Gyroelongated pentagonal birotunda
| [[Image:Johnson solid 48 net.png|80px]]
| [[Image:Gyroelongated pentagonal birotunda.png|80px]]
|-
| 49
| [[側錐三角柱]]
| Augmented triangular prism
| [[Image:Johnson solid 49 net.png|80px]]
| [[Image:Augmented triangular prism.png|80px]]
|-
| 50
| [[二側錐三角柱]]
| Biaugmented triangular prism
| [[Image:Johnson solid 50 net.png|80px]]
| [[Image:Biaugmented triangular prism.png|80px]]
|-
| 51
| [[三側錐三角柱]]
| Triaugmented triangular prism
| [[Image:Johnson solid 51 net.png|80px]]
| [[Image:Triaugmented triangular prism.png|80px]]
|-
| 52
| [[側錐五角柱]]
| Augmented pentagonal prism
| [[Image:Johnson solid 52 net.png|80px]]
| [[Image:Augmented pentagonal prism.png|80px]]
|-
| 53
| [[間二側錐五角柱]]
| Biaugmented pentagonal prism
| [[Image:Johnson solid 53 net.png|80px]]
| [[Image:Biaugmented pentagonal prism.png|80px]]
|-
| 54
| [[側錐六角柱]]
| Augmented hexagonal prism
| [[Image:Johnson solid 54 net.png|80px]]
| [[Image:Augmented hexagonal prism.png|80px]]
|-
| 55
| [[對二側錐六角柱]]
| Parabiaugmented hexagonal prism
| [[Image:Johnson solid 55 net.png|80px]]
| [[Image:Parabiaugmented hexagonal prism.png|80px]]
|-
| 56
| [[間二側錐六角柱]]
| Metabiaugmented hexagonal prism
| [[Image:Johnson solid 56 net.png|80px]]
| [[Image:Metabiaugmented hexagonal prism.png|80px]]
|-
| 57
| [[三側錐六角柱]]
| Triaugmented hexagonal prism
| [[Image:Johnson solid 57 net.png|80px]]
| [[Image:Triaugmented hexagonal prism.png|80px]]
|-
| 58
| {{link-en|侧锥正十二面体|Augmented dodecahedron}}
| Augmented dodecahedron
| [[Image:Johnson solid 58 net.png|80px]]
| [[Image:Augmented dodecahedron.png|80px]]
|-
| 59
| {{link-en|对二侧锥正十二面体|Parabiaugmented dodecahedron}}
| Parabiaugmented dodecahedron
| [[Image:Johnson solid 59 net.png|80px]]
| [[Image:Parabiaugmented dodecahedron.png|80px]]
|-
| 60
| {{link-en|间二侧锥正十二面体|Metabiaugmented dodecahedron}}
| Metabiaugmented dodecahedron
| [[Image:Johnson solid 60 net.png|80px]]
| [[Image:Metabiaugmented dodecahedron.png|80px]]
|-
| 61
| {{link-en|三侧锥正十二面体|Triaugmented dodecahedron}}
| Triaugmented dodecahedron
| [[Image:Johnson solid 61 net.png|80px]]
| [[Image:Triaugmented dodecahedron.png|80px]]
|-
| 62
| {{link-en|正二十面體欠鄰二側錐|Metabidiminished icosahedron}}
| Metabidiminished icosahedron
| [[Image:Johnson solid 62 net.png|80px]]
| [[Image:Metabidiminished icosahedron.png|80px]]
|-
| 63
| {{link-en|正二十面體欠三側錐|Tridiminished icosahedron}}
| Tridiminished icosahedron
| [[Image:Johnson solid 63 net.png|80px]]
| [[Image:Tridiminished icosahedron.png|80px]]
|-
| 64
| {{link-en|側錐正二十面體欠三側錐|Augmented tridiminished icosahedron}}
| Augmented tridiminished icosahedron
| [[Image:Johnson solid 64 net.png|80px]]
| [[Image:Augmented tridiminished icosahedron.png|80px]]
|-
| 65
| [[側台塔截角四面體]]
| Augmented truncated tetrahedron
| [[Image:Johnson solid 65 net.png|80px]]
| [[Image:Augmented truncated tetrahedron.png|80px]]
|-
| 66
| [[側台塔截角立方體]]
| Augmented truncated cube
| [[Image:Johnson solid 66 net.png|80px]]
| [[Image:Augmented truncated cube.png|80px]]
|-
| 67
| [[對二側帳塔截角立方體]]
| Biaugmented truncated cube
| [[Image:Johnson solid 67 net.png|80px]]
| [[Image:Biaugmented truncated cube.png|80px]]
|-
| 68
| {{link-en|側台塔截角十二面體|Augmented truncated dodecahedron}}
| Augmented truncated dodecahedron
| [[Image:Johnson solid 68 net.png|80px]]
| [[Image:Augmented truncated dodecahedron.png|80px]]
|-
| 69
| {{link-en|對二側台塔截角十二面體|Parabiaugmented truncated dodecahedron}}
| Parabiaugmented truncated dodecahedron
| [[Image:Johnson solid 69 net.png|80px]]
| [[Image:Parabiaugmented truncated dodecahedron.png|80px]]
|-
| 70
| {{link-en|間二側台塔截角十二面體|Metabiaugmented truncated dodecahedron}}
| Metabiaugmented truncated dodecahedron
| [[Image:Johnson solid 70 net.png|80px]]
| [[Image:Metabiaugmented truncated dodecahedron.png|80px]]
|-
| 71
| {{link-en|三側台塔截角十二面體|Triaugmented truncated dodecahedron}}
| Triaugmented truncated dodecahedron
| [[Image:Johnson solid 71 net.png|80px]]
| [[Image:Triaugmented truncated dodecahedron.png|80px]]
|-
| 72
| {{link-en|單旋側帳塔小斜方截半二十面體|Gyrate rhombicosidodecahedron}}
| Gyrate rhombicosidodecahedron
| [[Image:Johnson solid 72 net.png|80px]]
| [[Image:Gyrate rhombicosidodecahedron.png|80px]]
|-
| 73
| {{link-en|對二旋側台塔小斜方截半二十面體|Parabigyrate rhombicosidodecahedron}}
| Parabigyrate rhombicosidodecahedron
| [[Image:Johnson solid 73 net.png|80px]]
| [[Image:Parabigyrate rhombicosidodecahedron.png|80px]]
|-
| 74
| {{link-en|鄰二旋側台塔小斜方截半二十面體|Metabigyrate rhombicosidodecahedron}}
| Metabigyrate rhombicosidodecahedron
| [[Image:Johnson solid 74 net.png|80px]]
| [[Image:Metabigyrate rhombicosidodecahedron.png|80px]]
|-
| 75
| {{link-en|三旋側台塔小斜方截半二十面體|Trigyrate rhombicosidodecahedron}}
| Trigyrate rhombicosidodecahedron
| [[Image:Johnson solid 75 net.png|80px]]
| [[Image:Trigyrate rhombicosidodecahedron.png|80px]]
|-
| 76
| {{link-en|小斜方截半二十面體欠一側台塔|Diminished rhombicosidodecahedron}}
| Diminished rhombicosidodecahedron
| [[Image:Johnson solid 76 net.png|80px]]
| [[Image:Diminished rhombicosidodecahedron.png|80px]]
|-
| 77
| {{link-en|對單旋側台塔小斜方截半二十面體欠一側台塔|Paragyrate diminished rhombicosidodecahedron}}
| Paragyrate diminished rhombicosidodecahedron
| [[Image:Johnson solid 77 net.png|80px]]
| [[Image:Paragyrate diminished rhombicosidodecahedron.png|80px]]
|-
| 78
| {{link-en|鄰單旋側台塔小斜方截半二十面體欠一側台塔|Metagyrate diminished rhombicosidodecahedron}}
| Metagyrate diminished rhombicosidodecahedron
| [[Image:Johnson solid 78 net.png|80px]]
| [[Image:Metagyrate diminished rhombicosidodecahedron.png|80px]]
|-
| 79
| {{link-en|二旋側台塔小斜方截半二十面體欠一側台塔|Bigyrate diminished rhombicosidodecahedron}}
| Bigyrate diminished rhombicosidodecahedron
| [[Image:Johnson solid 79 net.png|80px]]
| [[Image:Bigyrate diminished rhombicosidodecahedron.png|80px]]
|-
| 80
| [[小斜方截半二十面體欠對二側帳塔]]
| Parabidiminished rhombicosidodecahedron
| [[Image:Johnson solid 80 net.png|80px]]
| [[Image:Parabidiminished rhombicosidodecahedron.png|80px]]
|-
| 81
| {{link-en|小斜方截半二十面體欠鄰二側帳塔|Metabidiminished rhombicosidodecahedron}}
| Metabidiminished rhombicosidodecahedron
| [[Image:Johnson solid 81 net.png|80px]]
| [[Image:Metabidiminished rhombicosidodecahedron.png|80px]]
|-
| 82
| [[單旋側台塔小斜方截半二十面體欠二側台塔]]
| Gyrate bidiminished rhombicosidodecahedron
| [[Image:Johnson solid 82 net.png|80px]]
| [[Image:Gyrate bidiminished rhombicosidodecahedron.png|80px]]
|-
| 83
| [[小斜方截半二十面體欠三側台塔]]
| Tridiminished rhombicosidodecahedron
| [[Image:Johnson solid 83 net.png|80px]]
| [[Image:Tridiminished rhombicosidodecahedron.png|80px]]
|-
| 84
| [[扭稜鍥形體]]
| Snub disphenoid
| [[Image:Johnson solid 84 net.png|80px]]
| [[Image:Snub disphenoid.png|80px]]
|-
| 85
| [[扭稜四角反角柱]]
| Snub square antiprism
| [[Image:Johnson solid 85 net.png|80px]]
| [[Image:Snub square antiprism.png|80px]]
|-
| 86
| [[球狀屋頂]]
| Sphenocorona
| [[Image:Johnson solid 86 net.png|80px]]
| [[Image:Sphenocorona.png|80px]]
|-
| 87
| [[側錐球狀屋頂]]
| Augmented sphenocorona
| [[Image:Johnson solid 87 net.png|80px]]
| [[Image:Augmented sphenocorona.png|80px]]
|-
| 88
| [[加長型球狀屋頂]]
| Sphenomegacorona
| [[Image:Johnson solid 88 net.png|80px]]
| [[Image:Sphenomegacorona.png|80px]]
|-
| 89
| [[廣底加長型球狀屋頂]]
| Hebesphenomegacorona
| [[Image:Johnson solid 89 net.png|80px]]
| [[Image:Hebesphenomegacorona.png|80px]]
|-
| 90
| [[五角錐球狀屋頂]]
| Disphenocingulum
| [[Image:Johnson solid 90 net.png|80px]]
| [[Image:Disphenocingulum.png|80px]]
|-
| 91
| [[雙新月雙罩帳]]
| Bilunabirotunda
| [[Image:Johnson solid 91 net.png|80px]]
| [[Image:Bilunabirotunda.png|80px]]
|-
| 92
| [[三角廣底球狀罩帳]]
| Triangular hebesphenorotunda
| [[Image:Johnson solid 92 net.png|80px]]
| [[Image:Triangular hebesphenorotunda.png|80px]]
|}
{{right|[[#top|返回頂部]]、[[#列表|表格頂部]] [[File:WWC arrow up.png|link=#top]]}}
說明：
* {{math|''J''<sub>''n''</sub>}} – 詹森多面體編號
* [[展開圖]] – 立體[[展開 (幾何)|展開]]成平面的結果

== 頂點、邊、面和對稱性 ==
下表列出詹森多面體的[[頂點 (幾何)|頂點]]數、邊數和面數，以及特定形狀的面數。同時也列出了其對稱性：
{| class="wikitable sortable" width=100%
|-
! {{math|''J''<sub>''n''</sub>}}
! 名稱
! 圖像
! V
! E
! F
! F<sub>3</sub>
! F<sub>4</sub>
! F<sub>5</sub>
! F<sub>6</sub>
! F<sub>8</sub>
! F<sub>10</sub>
! {{link-en|球面對稱群列表|List of spherical symmetry groups|對稱群}}
!{{link-en|對稱階數|Symmetry number|階數}}
|-
| 1
| [[正四角錐]]
| [[Image:Square pyramid.png|30px]]
| 5
| 8
| 5
| 4
| 1
|
|
|
|
| ''C''<sub>4v</sub>, [4], (*44)||8
|-
| 2
| [[正五角錐]]
| [[Image:Pentagonal pyramid.png|30px]]
| 6
| 10
| 6
| 5
|
| 1
|
|
|
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 3
| [[正三角帳塔]]
| [[Image:Triangular cupola.png|30px]]
| 9
| 15
| 8
| 4
| 3
|
| 1
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 4
| [[正四角帳塔]]
| [[Image:Square cupola.png|30px]]
| 12
| 20
| 10
| 4
| 5
|
|
| 1
|
| ''C''<sub>4v</sub>, [4], (*44)||8
|-
| 5
| [[正五角帳塔]]
| [[Image:Pentagonal cupola.png|30px]]
| 15
| 25
| 12
| 5
| 5
| 1
|
|
| 1
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 6
| [[正五角罩帳]]
| [[Image:Pentagonal rotunda.png|30px]]
| 20
| 35
| 17
| 10
|
| 6
|
|
| 1
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 7
| [[正三角錐柱]]
| [[Image:Elongated triangular pyramid.png|30px]]
| 7
| 12
| 7
| 4
| 3
|
|
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 8
| [[正四角錐柱]]
| [[Image:Elongated square pyramid.png|30px]]
| 9
| 16
| 9
| 4
| 5
|
|
|
|
| ''C''<sub>4v</sub>, [4], (*44)||8
|-
| 9
| [[正五角錐柱]]
| [[Image:Elongated pentagonal pyramid.png|30px]]
| 11
| 20
| 11
| 5
| 5
| 1
|
|
|
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 10
| [[四角錐反角柱]]
| [[Image:Gyroelongated square pyramid.png|30px]]
| 9
| 20
| 13
| 12
| 1
|
|
|
|
| ''C''<sub>4v</sub>, [4], (*44)||8
|-
| 11
| [[五角錐反角柱]]
| [[Image:Gyroelongated pentagonal pyramid.png|30px]]
| 11
| 25
| 16
| 15
|
| 1
|
|
|
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 12
| [[雙三角錐]]
| [[Image:Triangular dipyramid.png|30px]]
| 5
| 9
| 6
| 6
|
|
|
|
|
| ''D''<sub>3h</sub>, [3,2], (*223)||12
|-
| 13
| [[雙五角錐]]
| [[Image:Pentagonal dipyramid.png|30px]]
| 7
| 15
| 10
| 10
|
|
|
|
|
| ''D''<sub>5h</sub>, [5,2], (*225)||20
|-
| 14
| [[雙三角錐柱]]
| [[Image:Elongated triangular dipyramid.png|30px]]
| 8
| 15
| 9
| 6
| 3
|
|
|
|
| ''D''<sub>3h</sub>, [3,2], (*223)||12
|-
| 15
| [[雙四角錐柱]]
| [[Image:Elongated square dipyramid.png|30px]]
| 10
| 20
| 12
| 8
| 4
|
|
|
|
| ''D''<sub>4h</sub>, [4,2], (*224)||16
|-
| 16
| [[雙五角錐柱]]
| [[Image:Elongated pentagonal dipyramid.png|30px]]
| 12
| 25
| 15
| 10
| 5
|
|
|
|
| ''D''<sub>5h</sub>, [5,2], (*225)||20
|-
| 17
| [[雙四角錐反角柱]]
| [[Image:Gyroelongated square dipyramid.png|30px]]
| 10
| 24
| 16
| 16
|
|
|
|
|
| ''D''<sub>4d</sub>, [2<sup>+</sup>,8], (2*4)||16
|-
| 18
| [[三角帳塔柱]]
| [[Image:Elongated triangular cupola.png|30px]]
| 15
| 27
| 14
| 4
| 9
|
| 1
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 19
| [[四角帳塔柱]]
| [[Image:Elongated square cupola.png|30px]]
| 20
| 36
| 18
| 4
| 13
|
|
| 1
|
| ''C''<sub>4v</sub>, [4], (*44)||8
|-
| 20
| [[五角帳塔柱]]
| [[Image:Elongated pentagonal cupola.svg|30px]]
| 25
| 45
| 22
| 5
| 15
| 1
|
|
| 1
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 21
| [[正五角罩帳柱]]
| [[Image:Elongated pentagonal rotunda.png|30px]]
| 30
| 55
| 27
| 10
| 10
| 6
|
|
| 1
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 22
| [[正三角帳塔反角柱]]
| [[Image:Gyroelongated triangular cupola.png|30px]]
| 15
| 33
| 20
| 16
| 3
|
| 1
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 23
| [[正四角帳塔反角柱]]
| [[Image:Gyroelongated square cupola.png|30px]]
| 20
| 44
| 26
| 20
| 5
|
|
| 1
|
| ''C''<sub>4v</sub>, [4], (*44)||8
|-
| 24
| [[正五角台塔反角柱]]
| [[Image:Gyroelongated pentagonal cupola.png|30px]]
| 25
| 55
| 32
| 25
| 5
| 1
|
|
| 1
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 25
| [[正五角罩帳反角柱]]
| [[Image:Gyroelongated pentagonal rotunda.png|30px]]
| 30
| 65
| 37
| 30
|
| 6
|
|
| 1
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 26
| [[異相雙三角柱]]
| [[Image:Gyrobifastigium.png|30px]]
| 8
| 14
| 8
| 4
| 4
|
|
|
|
| ''D''<sub>2d</sub>, [2<sup>+</sup>,4], (2*2)||8
|-
| 27
| [[同相雙三角台塔]]
| [[Image:Triangular orthobicupola.png|30px]]
| 12
| 24
| 14
| 8
| 6
|
|
|
|
| ''D''<sub>3h</sub>, [3,2], (*223)||12
|-
| 28
| [[同相雙四角台塔]]
| [[Image:Square orthobicupola.png|30px]]
| 16
| 32
| 18
| 8
| 10
|
|
|
|
| ''D''<sub>4h</sub>, [4,2], (*224)||16
|-
| 29
| [[異相雙四角台塔]]
| [[Image:Square gyrobicupola.png|30px]]
| 16
| 32
| 18
| 8
| 10
|
|
|
|
| ''D''<sub>4d</sub>, [2<sup>+</sup>,8], (2*4)||16
|-
| 30
| [[同相雙五角台塔]]
| [[Image:Pentagonal orthobicupola.png|30px]]
| 20
| 40
| 22
| 10
| 10
| 2
|
|
|
| ''D''<sub>5h</sub>, [5,2], (*225)||20
|-
| 31
| [[異相雙五角台塔]]
| [[Image:Pentagonal gyrobicupola.png|30px]]
| 20
| 40
| 22
| 10
| 10
| 2
|
|
|
| ''D''<sub>5d</sub>, [2<sup>+</sup>,10], (2*5)||20
|-
| 32
| [[同相五角台塔丸塔]]
| [[Image:Pentagonal orthocupolarotunda.png|30px]]
| 25
| 50
| 27
| 15
| 5
| 7
|
|
|
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 33
| [[異相五角台塔丸塔]]
| [[Image:Pentagonal gyrocupolarotunda.png|30px]]
| 25
| 50
| 27
| 15
| 5
| 7
|
|
|
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 34
| {{link-en|同相雙五角丸塔|Pentagonal orthobirotunda}}
| [[Image:Pentagonal orthobirotunda.png|30px]]
| 30
| 60
| 32
| 20
|
| 12
|
|
|
| ''D''<sub>5h</sub>, [5,2], (*225)||20
|-
| 35
| {{link-en|同相雙三角台塔柱|Elongated triangular orthobicupola}}
| [[Image:Elongated triangular orthobicupola.png|30px]]
| 18
| 36
| 20
| 8
| 12
|
|
|
|
| ''D''<sub>3h</sub>, [3,2], (*223)||12
|-
| 36
| {{link-en|異相雙三角台塔柱|Elongated triangular gyrobicupola}}
| [[Image:Elongated triangular gyrobicupola.png|30px]]
| 18
| 36
| 20
| 8
| 12
|
|
|
|
| ''D''<sub>3d</sub>, [2<sup>+</sup>,6], (2*3)||12
|-
| 37
| [[異相雙四角台塔柱]]
| [[Image:Elongated square gyrobicupola.png|30px]]
| 24
| 48
| 26
| 8
| 18
|
|
|
|
| ''D''<sub>4d</sub>, [2<sup>+</sup>,8], (2*4)||16
|-
| 38
| {{link-en|同相雙五角台塔柱|Elongated pentagonal orthobicupola}}
| [[Image:Elongated pentagonal orthobicupola.png|30px]]
| 30
| 60
| 32
| 10
| 20
| 2
|
|
|
| ''D''<sub>5h</sub>, [5,2], (*225)||20
|-
| 39
| {{link-en|異相雙五角台塔柱|Elongated pentagonal gyrobicupola}}
| [[Image:Elongated pentagonal gyrobicupola.png|30px]]
| 30
| 60
| 32
| 10
| 20
| 2
|
|
|
| ''D''<sub>5d</sub>, [2<sup>+</sup>,10], (2*5)||20
|-
| 40
| {{link-en|同相五角台塔丸塔柱|Elongated pentagonal orthocupolarotunda}}
| [[Image:Elongated pentagonal orthocupolarotunda.png|30px]]
| 35
| 70
| 37
| 15
| 15
| 7
|
|
|
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 41
| {{link-en|異相五角台塔丸塔柱|Elongated pentagonal gyrocupolarotunda}}
| [[Image:Elongated pentagonal gyrocupolarotunda.png|30px]]
| 35
| 70
| 37
| 15
| 15
| 7
|
|
|
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 42
| {{link-en|同相五角雙丸塔柱|Elongated pentagonal orthobirotunda}}
| [[Image:Elongated pentagonal orthobirotunda.png|30px]]
| 40
| 80
| 42
| 20
| 10
| 12
|
|
|
| ''D''<sub>5h</sub>, [5,2], (*225)||20
|-
| 43
| {{link-en|異相五角雙丸塔柱|Elongated pentagonal gyrobirotunda}}
| [[Image:Elongated pentagonal gyrobirotunda.png|30px]]
| 40
| 80
| 42
| 20
| 10
| 12
|
|
|
| ''D''<sub>5d</sub>, [2<sup>+</sup>,10], (2*5)||20
|-
| 44
| {{link-en|雙三角台塔反角柱|Gyroelongated triangular bicupola}}
| [[Image:Gyroelongated triangular bicupola.png|30px]]
| 18
| 42
| 26
| 20
| 6
|
|
|
|
| ''D''<sub>3</sub>, [3,2]<sup>+</sup>,(223)||6
|-
| 45
| {{link-en|雙四角台塔反角柱|Gyroelongated square bicupola}}
| [[Image:Gyroelongated square bicupola.png|30px]]
| 24
| 56
| 34
| 24
| 10
|
|
|
|
| ''D''<sub>4</sub>, [4,2]<sup>+</sup>, (224)||8
|-
| 46
| {{link-en|雙五角台塔反角柱|Gyroelongated pentagonal bicupola}}
| [[Image:Gyroelongated pentagonal bicupola.png|30px]]
| 30
| 70
| 42
| 30
| 10
| 2
|
|
|
| ''D''<sub>5</sub>, [5,2]<sup>+</sup>, (225)||10
|-
| 47
| {{link-en|五角台塔丸塔反角柱|Gyroelongated pentagonal cupolarotunda}}
| [[Image:Gyroelongated pentagonal cupolarotunda.png|30px]]
| 35
| 80
| 47
| 35
| 5
| 7
|
|
|
| ''C''<sub>5</sub>, [5]<sup>+</sup>, (55)||5
|-
| 48
| {{link-en|雙五角丸塔反角柱|Gyroelongated pentagonal birotunda}}
| [[Image:Gyroelongated pentagonal birotunda.png|30px]]
| 40
| 90
| 52
| 40
|
| 12
|
|
|
| ''D''<sub>5</sub>, [5,2]<sup>+</sup>, (225)||10
|-
| 49
| [[側錐三角柱]]
| [[Image:Augmented triangular prism.png|30px]]
| 7
| 13
| 8
| 6
| 2
|
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 50
| [[二側錐三角柱]]
| [[Image:Biaugmented triangular prism.png|30px]]
| 8
| 17
| 11
| 10
| 1
|
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 51
| [[三側錐三角柱]]
| [[Image:Triaugmented triangular prism.png|30px]]
| 9
| 21
| 14
| 14
|
|
|
|
|
| ''D''<sub>3h</sub>, [3,2], (*223)||12
|-
| 52
| [[側錐五角柱]]
| [[Image:Augmented pentagonal prism.png|30px]]
| 11
| 19
| 10
| 4
| 4
| 2
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 53
| [[間二側錐五角柱]]
| [[Image:Biaugmented pentagonal prism.png|30px]]
| 12
| 23
| 13
| 8
| 3
| 2
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 54
| [[側錐六角柱]]
| [[Image:Augmented hexagonal prism.png|30px]]
| 13
| 22
| 11
| 4
| 5
|
| 2
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 55
| [[對二側錐六角柱]]
| [[Image:Parabiaugmented hexagonal prism.png|30px]]
| 14
| 26
| 14
| 8
| 4
|
| 2
|
|
| ''D''<sub>2h</sub>, [2,2], (*222)||8
|-
| 56
| [[間二側錐六角柱]]
| [[Image:Metabiaugmented hexagonal prism.png|30px]]
| 14
| 26
| 14
| 8
| 4
|
| 2
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 57
| [[三側錐六角柱]]
| [[Image:Triaugmented hexagonal prism.png|30px]]
| 15
| 30
| 17
| 12
| 3
|
| 2
|
|
| ''D''<sub>3h</sub>, [3,2], (*223)||12
|-
| 58
| {{link-en|侧锥正十二面体|Augmented dodecahedron}}
| [[Image:Augmented dodecahedron.png|30px]]
| 21
| 35
| 16
| 5
|
| 11
|
|
|
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 59
| {{link-en|对二侧锥正十二面体|Parabiaugmented dodecahedron}}
| [[Image:Parabiaugmented dodecahedron.png|30px]]
| 22
| 40
| 20
| 10
|
| 10
|
|
|
| ''D''<sub>5d</sub>, [2<sup>+</sup>,10], (2*5)||20
|-
| 60
| {{link-en|间二侧锥正十二面体|Metabiaugmented dodecahedron}}
| [[Image:Metabiaugmented dodecahedron.png|30px]]
| 22
| 40
| 20
| 10
|
| 10
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 61
| {{link-en|三侧锥正十二面体|Triaugmented dodecahedron}}
| [[Image:Triaugmented dodecahedron.png|30px]]
| 23
| 45
| 24
| 15
|
| 9
|
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 62
| {{link-en|正二十面體欠鄰二側錐|Metabidiminished icosahedron}}
| [[Image:Metabidiminished icosahedron.png|30px]]
| 10
| 20
| 12
| 10
|
| 2
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 63
| {{link-en|正二十面體欠三側錐|Tridiminished icosahedron}}
| [[Image:Tridiminished icosahedron.png|30px]]
| 9
| 15
| 8
| 5
|
| 3
|
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 64
| {{link-en|側錐正二十面體欠三側錐|Augmented tridiminished icosahedron}}
| [[Image:Augmented tridiminished icosahedron.png|30px]]
| 10
| 18
| 10
| 7
|
| 3
|
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 65
| [[側台塔截角四面體]]
| [[Image:Augmented truncated tetrahedron.png|30px]]
| 15
| 27
| 14
| 8
| 3
|
| 3
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 66
| [[側台塔截角立方體]]
| [[Image:Augmented truncated cube.png|30px]]
| 28
| 48
| 22
| 12
| 5
|
|
| 5
|
| ''C''<sub>4v</sub>, [4], (*44)||8
|-
| 67
| [[對二側帳塔截角立方體]]
| [[Image:Biaugmented truncated cube.png|30px]]
| 32
| 60
| 30
| 16
| 10
|
|
| 4
|
| ''D''<sub>4h</sub>, [4,2], (*224)||16
|-
| 68
| {{link-en|側台塔截角十二面體|Augmented truncated dodecahedron}}
| [[Image:Augmented truncated dodecahedron.png|30px]]
| 65
| 105
| 42
| 25
| 5
| 1
|
|
| 11
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 69
| {{link-en|對二側台塔截角十二面體|Parabiaugmented truncated dodecahedron}}
| [[Image:Parabiaugmented truncated dodecahedron.png|30px]]
| 70
| 120
| 52
| 30
| 10
| 2
|
|
| 10
| ''D''<sub>5d</sub>, [2<sup>+</sup>,10], (2*5)||20
|-
| 70
| {{link-en|間二側台塔截角十二面體|Metabiaugmented truncated dodecahedron}}
| [[Image:Metabiaugmented truncated dodecahedron.png|30px]]
| 70
| 120
| 52
| 30
| 10
| 2
|
|
| 10
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 71
| {{link-en|三側台塔截角十二面體|Triaugmented truncated dodecahedron}}
| [[Image:Triaugmented truncated dodecahedron.png|30px]]
| 75
| 135
| 62
| 35
| 15
| 3
|
|
| 9
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 72
| {{link-en|單旋側帳塔小斜方截半二十面體|Gyrate rhombicosidodecahedron}}
| [[Image:Gyrate rhombicosidodecahedron.png|30px]]
| 60
| 120
| 62
| 20
| 30
| 12
|
|
|
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 73
| {{link-en|對二旋側台塔小斜方截半二十面體|Parabigyrate rhombicosidodecahedron}}
| [[Image:Parabigyrate rhombicosidodecahedron.png|30px]]
| 60
| 120
| 62
| 20
| 30
| 12
|
|
|
| ''D''<sub>5d</sub>, [2<sup>+</sup>,10], (2*5)||20
|-
| 74
| {{link-en|鄰二旋側台塔小斜方截半二十面體|Metabigyrate rhombicosidodecahedron}}
| [[Image:Metabigyrate rhombicosidodecahedron.png|30px]]
| 60
| 120
| 62
| 20
| 30
| 12
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 75
| {{link-en|三旋側台塔小斜方截半二十面體|Trigyrate rhombicosidodecahedron}}
| [[Image:Trigyrate rhombicosidodecahedron.png|30px]]
| 60
| 120
| 62
| 20
| 30
| 12
|
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 76
| {{link-en|小斜方截半二十面體欠一側台塔|Diminished rhombicosidodecahedron}}
| [[Image:Diminished rhombicosidodecahedron.png|30px]]
| 55
| 105
| 52
| 15
| 25
| 11
|
|
| 1
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 77
| {{link-en|對單旋側台塔小斜方截半二十面體欠一側台塔|Paragyrate diminished rhombicosidodecahedron}}
| [[Image:Paragyrate diminished rhombicosidodecahedron.png|30px]]
| 55
| 105
| 52
| 15
| 25
| 11
|
|
| 1
| ''C''<sub>5v</sub>, [5], (*55)||10
|-
| 78
| {{link-en|鄰單旋側台塔小斜方截半二十面體欠一側台塔|Metagyrate diminished rhombicosidodecahedron}}
| [[Image:Metagyrate diminished rhombicosidodecahedron.png|30px]]
| 55
| 105
| 52
| 15
| 25
| 11
|
|
| 1
| ''C''<sub>s</sub>, [&nbsp;], (*11)||2
|-
| 79
| {{link-en|二旋側台塔小斜方截半二十面體欠一側台塔|Bigyrate diminished rhombicosidodecahedron}}
| [[Image:Bigyrate diminished rhombicosidodecahedron.png|30px]]
| 55
| 105
| 52
| 15
| 25
| 11
|
|
| 1
| ''C''<sub>s</sub>, [&nbsp;], (*11)||2
|-
| 80
| [[小斜方截半二十面體欠對二側帳塔]]
| [[Image:Parabidiminished rhombicosidodecahedron.png|30px]]
| 50
| 90
| 42
| 10
| 20
| 10
|
|
| 2
| ''D''<sub>5d</sub>, [2<sup>+</sup>,10], (2*5)||20
|-
| 81
| {{link-en|小斜方截半二十面體欠鄰二側帳塔|Metabidiminished rhombicosidodecahedron}}
| [[Image:Metabidiminished rhombicosidodecahedron.png|30px]]
| 50
| 90
| 42
| 10
| 20
| 10
|
|
| 2
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 82
| [[單旋側台塔小斜方截半二十面體欠二側台塔]]
| [[Image:Gyrate bidiminished rhombicosidodecahedron.png|30px]]
| 50
| 90
| 42
| 10
| 20
| 10
|
|
| 2
| ''C''<sub>s</sub>, [&nbsp;], (*11)||2
|-
| 83
| [[小斜方截半二十面體欠三側台塔]]
| [[Image:Tridiminished rhombicosidodecahedron.png|30px]]
| 45
| 75
| 32
| 5
| 15
| 9
|
|
| 3
| ''C''<sub>3v</sub>, [3], (*33)||6
|-
| 84
| [[扭稜鍥形體]]
| [[Image:Snub disphenoid.png|30px]]
| 8
| 18
| 12
| 12
|
|
|
|
|
| ''D''<sub>2d</sub>, [2<sup>+</sup>,4], (2*2)||8
|-
| 85
| [[扭稜四角反角柱]]
| [[Image:Snub square antiprism.png|30px]]
| 16
| 40
| 26
| 24
| 2
|
|
|
|
| ''D''<sub>4d</sub>, [2<sup>+</sup>,8], (2*4)||16
|-
| 86
| [[球狀屋頂]]
| [[Image:Sphenocorona.png|30px]]
| 10
| 22
| 14
| 12
| 2
|
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 87
| [[側錐球狀屋頂]]
| [[Image:Augmented sphenocorona.png|30px]]
| 11
| 26
| 17
| 16
| 1
|
|
|
|
| ''C''<sub>s</sub>, [&nbsp;], (*11)||2
|-
| 88
| [[加長型球狀屋頂]]
| [[Image:Sphenomegacorona.png|30px]]
| 12
| 28
| 18
| 16
| 2
|
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 89
| [[廣底加長型球狀屋頂]]
| [[Image:Hebesphenomegacorona.png|30px]]
| 14
| 33
| 21
| 18
| 3
|
|
|
|
| ''C''<sub>2v</sub>, [2], (*22)||4
|-
| 90
| [[五角錐球狀屋頂]]
| [[Image:Disphenocingulum.png|30px]]
| 16
| 38
| 24
| 20
| 4
|
|
|
|
| ''D''<sub>2d</sub>, [2<sup>+</sup>,4], (2*2)||8
|-
| 91
| [[雙新月雙罩帳]]
| [[Image:Bilunabirotunda.png|30px]]
| 14
| 26
| 14
| 8
| 2
| 4
|
|
|
| ''D''<sub>2h</sub>, [2,2], (*222)||8
|-
| 92
| [[三角廣底球狀罩帳]]
| [[Image:Triangular hebesphenorotunda.png|30px]]
| 18
| 36
| 20
| 13
| 3
| 3
| 1
|
|
| ''C''<sub>3v</sub>, [3], (*33)||6
|}
{{right|[[#top|返回頂部]]、[[#頂點、邊、面和對稱性|表格頂部]] [[File:WWC arrow up.png|link=#top]]}}
說明：
* {{math|''J''<sub>''n''</sub>}} – 詹森多面體編號
* V – [[頂點 (幾何)|頂點]]的數量
* E – [[邊 (幾何)|邊]]的數量
* F – [[面 (幾何)|面]]（所有的面）的數量
* F<sub>n</sub> – 僅n邊形[[面 (幾何)|面]]的數量
* F<sub>3</sub>～F<sub>10</sub> – F<sub>3</sub>：面為三角形的面的數量、F<sub>4</sub>：面為正方形的面的數量……以此類推

其中，[[正四角錐]]（{{math|''J''<sub>1</sub>}}）有最少的頂點（5個）、最少的邊（8條）和最少的面（5個）。

{{link-en|三側台塔截角十二面體|Triaugmented truncated dodecahedron}}{{math|''J''<sub>71</sub>}}具有最多的頂點（75個）和最多的邊（135條）。 它的面數也是最多的（62個），其他還有{{link-en|單旋側帳塔小斜方截半二十面體|Gyrate rhombicosidodecahedron}}{{math|''J''<sub>72</sub>}}、{{link-en|對二旋側台塔小斜方截半二十面體|Parabigyrate rhombicosidodecahedron}}{{math|''J''<sub>73</sub>}}、{{link-en|鄰二旋側台塔小斜方截半二十面體|Metabigyrate rhombicosidodecahedron}}{{math|''J''<sub>74</sub>}}和{{link-en|三旋側台塔小斜方截半二十面體|Trigyrate rhombicosidodecahedron}}{{math|''J''<sub>75</sub>}}。

== 表面積 ==
由於詹森多面體的所有面都是由正三角形、正方形、正五邊形、正六邊形、正八邊形或正十邊形所組成，代表著其面的邊數僅會有3、4、5、6、8或10條，且為正多邊形，因此這些正多邊形面都會具有相同的邊長{{math|''a''}}，因此詹森多面體的表面積{{math|''A''}}可由下式計算得到：
:<math>A=\sum_{n=3,4,5,6,8,10}F_n A_n</math>
其中 {{math|''F''<sub>''n''</sub>}}是上表中的多邊形面數，且正{{math|''n''}}邊形的面積{{math|''A''<sub>''n''</sub>}}也可由下式計算得到：
:<math>A_n = \left( \frac{n}{4} \cot{\frac{\pi}{n}} \right) a^2</math>
在詹森多面體的例子中，組成其的正多邊形僅有正三角形、正方形、正五邊形、正六邊形、正八邊形或正十邊形，而我們有正三角形的面積{{math|''A''<sub>''3''</sub>}}、正方形的面積{{math|''A''<sub>''4''</sub>}}、正五邊形的面積{{math|''A''<sub>''5''</sub>}}、正六邊形的面積{{math|''A''<sub>''6''</sub>}}、正八邊形{{math|''A''<sub>''8''</sub>}}的面積和正十邊形{{math|''A''<sub>''10''</sub>}}的面積公式：
:<math>A_3 = \frac{1}{4} \sqrt{3}\,a^2</math>
:<math>A_4 = a^2</math>
:<math>A_5 = \frac{1}{4} \sqrt{5(5 + 2\sqrt{5})}\,a^2</math>
:<math>A_6 = \frac{3}{2} \sqrt{3}\,a^2</math>
:<math>A_8 = 2(1 + \sqrt{2})\,a^2</math>
:<math>A_{10} = \frac{5}{2} \sqrt{5 + 2\sqrt{5}}\,a^2,</math>
因此可以得出下表的詹森多面體表面積。
{| class="wikitable sortable"
|-
! {{math|''J''<sub>''n''</sub>}}
! 多面體名稱
! {{math|''A''/''a''<sup>2</sup>}} （近似值）
! {{math|''A''/''a''<sup>2</sup>}} （精確值）
|-
| 1
| [[正四角錐]]
| 2.732050808
| <math>1+\sqrt{3}</math>
|-
| 2
| [[正五角錐]]
| 3.885540910
| <math>\frac{1}{4} \left(5 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 3
| [[正三角帳塔]]
| 7.330127019
| <math>\frac{1}{2} \left(6+5 \sqrt{3}\right)</math>
|-
| 4
| [[正四角帳塔]]
| 11.560477932
| <math>7+2 \sqrt{2}+\sqrt{3}</math>
|-
| 5
| [[正五角帳塔]]
| 16.579749753
| <math>\frac{1}{4} \left(20+5 \sqrt{3}+10 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 6
| [[正五角罩帳]]
| 22.347200265
| <math>\frac{1}{2} \left(5 \sqrt{3}+5 \sqrt{5+2 \sqrt{5}}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 7
| [[正三角錐柱]]
| 4.732050808
| <math>3+\sqrt{3}</math>
|-
| 8
| [[正四角錐柱]]
| 6.732050808
| <math>5+\sqrt{3}</math>
|-
| 9
| [[正五角錐柱]]
| 8.885540910
| <math>\frac{1}{4} \left(20+5 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 10
| [[正四角錐反角柱]]
| 6.196152423
| <math>1+3 \sqrt{3}</math>
|-
| 11
| [[正五角錐反角柱]]
| 8.215667929
| <math>\frac{1}{4} \left(15 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 12
| [[雙三角錐]]
| 2.598076211
| <math>\frac{3 \sqrt{3}}{2}</math>
|-
| 13
| [[雙五角錐]]
| 4.330127019
| <math>\frac{5 \sqrt{3}}{2}</math>
|-
| 14
| [[雙三角錐柱]]
| 5.598076211
| <math>\frac{3}{2} \left(2+\sqrt{3}\right)</math>
|-
| 15
| [[雙四角錐柱]]
| 7.464101615
| <math>2 \left(2+\sqrt{3}\right)</math>
|-
| 16
| [[雙五角錐柱]]
| 9.330127019
| <math>\frac{5}{2} \left(2+\sqrt{3}\right)</math>
|-
| 17
| [[雙四角錐反角柱]]
| 6.928203230
| <math>4 \sqrt{3}</math>
|-
| 18
| [[三角帳塔柱]]
| 13.330127019
| <math>\frac{1}{2} \left(18+5 \sqrt{3}\right)</math>
|-
| 19
| [[四角帳塔柱]]
| 19.560477932
| <math>15+2 \sqrt{2}+\sqrt{3}</math>
|-
| 20
| [[五角帳塔柱]]
| 26.579749753
| <math>\frac{1}{4} \left(60+5 \sqrt{3}+10 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 21
| [[正五角罩帳柱]]
| 32.347200265
| <math>\frac{1}{2} \left(20+5 \sqrt{3}+5 \sqrt{5+2 \sqrt{5}}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 22
| [[正三角帳塔反角柱]]
| 12.526279442
| <math>\frac{1}{2} \left(6+11 \sqrt{3}\right)</math>
|-
| 23
| [[正四角帳塔反角柱]]
| 18.488681163
| <math>7+2 \sqrt{2}+5 \sqrt{3}</math>
|-
| 24
| [[正五角台塔反角柱]]
| 25.240003791
| <math>\frac{1}{4} \left(20+25 \sqrt{3}+10 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 25
| [[正五角罩帳反角柱]]
| 31.007454303
| <math>\frac{1}{2} \left(15 \sqrt{3}+5 \sqrt{5+2 \sqrt{5}}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 26
| [[異相雙三角柱]]
| 5.732050808
| <math>4+\sqrt{3}</math>
|-
| 27
| [[同相雙三角台塔]]
| 9.464101615
| <math>2 \left(3+\sqrt{3}\right)</math>
|-
| 28
| [[同相雙四角台塔]]
| 13.464101615
| <math>2 \left(5+\sqrt{3}\right)</math>
|-
| 29
| [[異相雙四角台塔]]
| 13.464101615
| <math>2 \left(5+\sqrt{3}\right)</math>
|-
| 30
| [[同相雙五角台塔]]
| 17.771081820
| <math>\frac{1}{2} \left(20+5 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 31
| [[異相雙五角台塔]]
| 17.771081820
| <math>\frac{1}{2} \left(20+5 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 32
| [[同相五角台塔丸塔]]
| 23.538532333
| <math>\frac{1}{4} \left(20+15 \sqrt{3}+7 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 33
| [[異相五角台塔丸塔]]
| 23.538532333
| <math>\frac{1}{4} \left(20+15 \sqrt{3}+7 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 34
| {{link-en|同相雙五角丸塔|Pentagonal orthobirotunda}}
| 29.305982845
| <math>5 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}</math>
|-
| 35
| {{link-en|同相雙三角台塔柱|Elongated triangular orthobicupola}}
| 15.464101615
| <math>2 \left(6+\sqrt{3}\right)</math>
|-
| 36
| {{link-en|異相雙三角台塔柱|Elongated triangular gyrobicupola}}
| 15.464101615
| <math>2 \left(6+\sqrt{3}\right)</math>
|-
| 37
| [[異相雙四角台塔柱]]
| 21.464101615
| <math>2 \left(9+\sqrt{3}\right)</math>
|-
| 38
| {{link-en|同相雙五角台塔柱|Elongated pentagonal orthobicupola}}
| 27.771081820
| <math>\frac{1}{2} \left(40+5 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 39
| {{link-en|異相雙五角台塔柱|Elongated pentagonal gyrobicupola}}
| 27.771081820
| <math>\frac{1}{2} \left(40+5 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 40
| {{link-en|同相五角台塔丸塔柱|Elongated pentagonal orthocupolarotunda}}
| 33.538532333
| <math>\frac{1}{4} \left(60+15 \sqrt{3}+7 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 41
| {{link-en|異相五角台塔丸塔柱|Elongated pentagonal gyrocupolarotunda}}
| 33.538532333
| <math>\frac{1}{4} \left(60+15 \sqrt{3}+7 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 42
| {{link-en|同相五角雙丸塔柱|Elongated pentagonal orthobirotunda}}
| 39.305982845
| <math>10+5 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}</math>
|-
| 43
| {{link-en|異相五角雙丸塔柱|Elongated pentagonal gyrobirotunda}}
| 39.305982845
| <math>10+5 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}</math>
|-
| 44
| {{link-en|雙三角台塔反角柱|Gyroelongated triangular bicupola}}
| 14.660254038
| <math>6+5 \sqrt{3}</math>
|-
| 45
| {{link-en|雙四角台塔反角柱|Gyroelongated square bicupola}}
| 20.392304845
| <math>2 \left(5+3 \sqrt{3}\right)</math>
|-
| 46
| {{link-en|雙五角台塔反角柱|Gyroelongated pentagonal bicupola}}
| 26.431335858
| <math>\frac{1}{2} \left(20+15 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 47
| {{link-en|五角台塔丸塔反角柱|Gyroelongated pentagonal cupolarotunda}}
| 32.198786370
| <math>\frac{1}{4} \left(20+35 \sqrt{3}+7 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 48
| {{link-en|雙五角丸塔反角柱|Gyroelongated pentagonal birotunda}}
| 37.966236883
| <math>10 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}</math>
|-
| 49
| [[側錐三角柱]]
| 4.598076211
| <math>\frac{1}{2} \left(4+3 \sqrt{3}\right)</math>
|-
| 50
| [[二側錐三角柱]]
| 5.330127019
| <math>\frac{1}{2} \left(2+5 \sqrt{3}\right)</math>
|-
| 51
| [[三側錐三角柱]]
| 6.062177826
| <math>\frac{7 \sqrt{3}}{2}</math>
|-
| 52
| [[側錐五角柱]]
| 9.173005609
| <math>\frac{1}{2} \left(8+2 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 53
| [[間二側錐五角柱]]
| 9.905056416
| <math>\frac{1}{2} \left(6+4 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 54
| [[側錐六角柱]]
| 11.928203230
| <math>5+4 \sqrt{3}</math>
|-
| 55
| [[對二側錐六角柱]]
| 12.660254038
| <math>4+5 \sqrt{3}</math>
|-
| 56
| [[間二側錐六角柱]]
| 12.660254038
| <math>4+5 \sqrt{3}</math>
|-
| 57
| [[三側錐六角柱]]
| 13.392304845
| <math>3 \left(1+2 \sqrt{3}\right)</math>
|-
| 58
| {{link-en|侧锥正十二面体|Augmented dodecahedron}}
| 21.090314916
| <math>\frac{1}{4} \left(5 \sqrt{3}+11 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 59
| {{link-en|对二侧锥正十二面体|Parabiaugmented dodecahedron}}
| 21.534901025
| <math>\frac{5}{2} \left(\sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 60
| {{link-en|间二侧锥正十二面体|Metabiaugmented dodecahedron}}
| 21.534901025
| <math>\frac{5}{2} \left(\sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 61
| {{link-en|三侧锥正十二面体|Triaugmented dodecahedron}}
| 21.979487134
| <math>\frac{3}{4} \left(5 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 62
| {{link-en|正二十面體欠鄰二側錐|Metabidiminished icosahedron}}
| 7.771081820
| <math>\frac{1}{2} \left(5 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 63
| {{link-en|正二十面體欠三側錐|Tridiminished icosahedron}}
| 7.326495711
| <math>\frac{1}{4} \left(5 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 64
| {{link-en|側錐正二十面體欠三側錐|Augmented tridiminished icosahedron}}
| 8.192521115
| <math>\frac{1}{4} \left(7 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 65
| [[側台塔截角四面體]]
| 14.258330249
| <math>\frac{1}{2} \left(6+13 \sqrt{3}\right)</math>
|-
| 66
| [[側台塔截角立方體]]
| 34.338288046
| <math>15+10 \sqrt{2}+3 \sqrt{3}</math>
|-
| 67
| [[對二側帳塔截角立方體]]
| 36.241911729
| <math>2 \left(9+4 \sqrt{2}+2 \sqrt{3}\right)</math>
|-
| 68
| {{link-en|側台塔截角十二面體|Augmented truncated dodecahedron}}
| 102.182092220
| <math>\frac{1}{4} \left(20+25 \sqrt{3}+110 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 69
| {{link-en|對二側台塔截角十二面體|Parabiaugmented truncated dodecahedron}}
| 103.373424287
| <math>\frac{1}{2} \left(20+15 \sqrt{3}+50 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 70
| {{link-en|間二側台塔截角十二面體|Metabiaugmented truncated dodecahedron}}
| 103.373424287
| <math>\frac{1}{2} \left(20+15 \sqrt{3}+50 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 71
| {{link-en|三側台塔截角十二面體|Triaugmented truncated dodecahedron}}
| 104.564756354
| <math>\frac{1}{4} \left(60+35 \sqrt{3}+90 \sqrt{5+2 \sqrt{5}}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 72
| {{link-en|單旋側帳塔小斜方截半二十面體|Gyrate rhombicosidodecahedron}}
| 59.305982845
| <math>30+5 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}</math>
|-
| 73
| {{link-en|對二旋側台塔小斜方截半二十面體|Parabigyrate rhombicosidodecahedron}}
| 59.305982845
| <math>30+5 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}</math>
|-
| 74
| {{link-en|鄰二旋側台塔小斜方截半二十面體|Metabigyrate rhombicosidodecahedron}}
| 59.305982845
| <math>30+5 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}</math>
|-
| 75
| {{link-en|三旋側台塔小斜方截半二十面體|Trigyrate rhombicosidodecahedron}}
| 59.305982845
| <math>30+5 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}</math>
|-
| 76
| {{link-en|小斜方截半二十面體欠一側台塔|Diminished rhombicosidodecahedron}}
| 58.114650778
| <math>\frac{1}{4} \left(100+15 \sqrt{3}+10 \sqrt{5+2 \sqrt{5}}+11 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 77
| {{link-en|對單旋側台塔小斜方截半二十面體欠一側台塔|Paragyrate diminished rhombicosidodecahedron}}
| 58.114650778
| <math>\frac{1}{4} \left(100+15 \sqrt{3}+10 \sqrt{5+2 \sqrt{5}}+11 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 78
| {{link-en|鄰單旋側台塔小斜方截半二十面體欠一側台塔|Metagyrate diminished rhombicosidodecahedron}}
| 58.114650778
| <math>\frac{1}{4} \left(100+15 \sqrt{3}+10 \sqrt{5+2 \sqrt{5}}+11 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 79
| {{link-en|二旋側台塔小斜方截半二十面體欠一側台塔|Bigyrate diminished rhombicosidodecahedron}}
| 58.114650778
| <math>\frac{1}{4} \left(100+15 \sqrt{3}+10 \sqrt{5+2 \sqrt{5}}+11 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 80
| [[小斜方截半二十面體欠對二側帳塔]]
| 56.923318711
| <math>\frac{5}{2} \left(8+\sqrt{3}+2 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 81
| {{link-en|小斜方截半二十面體欠鄰二側帳塔|Metabidiminished rhombicosidodecahedron}}
| 56.923318711
| <math>\frac{5}{2} \left(8+\sqrt{3}+2 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 82
| [[單旋側台塔小斜方截半二十面體欠二側台塔]]
| 56.923318711
| <math>\frac{5}{2} \left(8+\sqrt{3}+2 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 83
| [[小斜方截半二十面體欠三側台塔]]
| 55.731986644
| <math>\frac{1}{4} \left(60+5 \sqrt{3}+30 \sqrt{5+2 \sqrt{5}}+9 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 84
| [[扭稜鍥形體]]
| 5.196152423
| <math>3 \sqrt{3}</math>
|-
| 85
| [[扭稜四角反角柱]]
| 12.392304845
| <math>2 \left(1+3 \sqrt{3}\right)</math>
|-
| 86
| [[球狀屋頂]]
| 7.196152423
| <math>2+3 \sqrt{3}</math>
|-
| 87
| [[側錐球狀屋頂]]
| 7.928203230
| <math>1+4 \sqrt{3}</math>
|-
| 88
| [[加長型球狀屋頂]]
| 8.928203230
| <math>2 \left(1+2 \sqrt{3}\right)</math>
|-
| 89
| [[廣底加長型球狀屋頂]]
| 10.794228634
| <math>\frac{3}{2} \left(2+3 \sqrt{3}\right)</math>
|-
| 90
| [[五角錐球狀屋頂]]
| 12.660254038
| <math>4+5 \sqrt{3}</math>
|-
| 91
| [[雙新月雙罩帳]]
| 12.346011217
| <math>2+2 \sqrt{3}+\sqrt{5 \left(5+2 \sqrt{5}\right)}</math>
|-
| 92
| [[三角廣底球狀罩帳]]
| 16.388673538
| <math>\frac{1}{4} \left(12+19 \sqrt{3}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|}
在固定邊長的條件下，[[雙三角錐]]{{math|''J''<sub>12</sub>}}的[[表面積]]最小，而{{link-en|三側台塔截角十二面體|Triaugmented truncated dodecahedron}}{{math|''J''<sub>71</sub>}}的表面積最大，兩者相差40倍以上。

== 體積 ==
下表列出了詹森多面體的體積。在這個表格中，{{math|''V''}}代表體積（不是第一個表中的頂點數），而{{math|''a''}}代表邊長。

表格的資料來源是[[沃尔夫勒姆研究公司]]的[[Mathematica]]軟體中提供的'''<syntaxhighlight lang=mathematica inline>PolyhedronData[..., "Volume"]</syntaxhighlight>'''計算多面體體積的指令。

詹森多面體的體積也可以根據其頂點座標來計算出來。如果邊長是固定的，那麼所有92個詹森多面體的頂點座標就都是已知的。如此一來，就可以用此資訊來計算體積。概念上最簡單的作法是：對要算體積的詹森多面體之表面做三角化，例如在每個非三角形面的中心添加一個額外的點，然後將之與該面的其他頂點連接構成多個三角形（並不是所有凸多面體都可以不添加額外頂點就完成{{link-en|三角剖分|Triangulation (geometry)}}<ref>{{cite web | url=http://www.ics.uci.edu/~eppstein/junkyard/untetra/ | title=Three Untetrahedralizable Objects | author={{link-en|大衛愛普斯坦|David Eppstein|D. Eppstein}} | website=www.ics.uci.edu | access-date=2022-05-25 | archive-date=2021-01-26 | archive-url=https://web.archive.org/web/20210126095003/https://www.ics.uci.edu/~eppstein/junkyard/untetra/ }}</ref>）。完成表面的三角化後選擇一些內部點作為“原點”，這樣就可以把表面的三角形與內部所選的點構造成不規則四面體。這些不規則四面體在多面體內部有一個頂點、在多面體表面有3個頂點，而詹森多面體的體積就是這些不規則四面體的體積總和。不規則四面體的體積可以透過公式計算。

{| class="wikitable sortable"
|-
! {{math|''J''<sub>''n''</sub>}}
! 多面體名稱
! {{math|''V''/''a''<sup>3</sup>}}（近似值）
! {{math|''V''/''a''<sup>3</sup>}}（精確值）
|-
| 1
| [[正四角錐]]
| 0.235702260
| <math>\frac{1}{3 \sqrt{2}}</math>
|-
| 2
| [[正五角錐]]
| 0.301502832
| <math>\frac{1}{24} \left(5+\sqrt{5}\right)</math>
|-
| 3
| [[正三角帳塔]]
| 1.178511302
| <math>\frac{5}{3 \sqrt{2}}</math>
|-
| 4
| [[正四角帳塔]]
| 1.942809042
| <math>1+\frac{2 \sqrt{2}}{3}</math>
|-
| 5
| [[正五角帳塔]]
| 2.324045318
| <math>\frac{1}{6} \left(5+4 \sqrt{5}\right)</math>
|-
| 6
| [[正五角罩帳]]
| 6.917762968
| <math>\frac{1}{12} \left(45+17 \sqrt{5}\right)</math>
|-
| 7
| [[正三角錐柱]]
| 0.550863832
| <math>\frac{1}{12} \left(\sqrt{2}+3 \sqrt{3}\right)</math>
|-
| 8
| [[正四角錐柱]]
| 1.235702260
| <math>\frac{1}{6} \left(6+\sqrt{2}\right)</math>
|-
| 9
| [[正五角錐柱]]
| 2.021980233
| <math>\frac{1}{24} \left(5+\sqrt{5}+6 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 10
| [[正四角錐反角柱]]
| 1.192702242
| <math>\frac{1}{6} \left(\sqrt{2}+2 \sqrt{4+3 \sqrt{2}}\right)</math>
|-
| 11
| [[正五角錐反角柱]]
| 1.880192158
| <math>\frac{1}{24} \left(25+9 \sqrt{5}\right)</math>
|-
| 12
| [[雙三角錐]]
| 0.235702260
| <math>\frac{1}{3 \sqrt{2}}</math>
|-
| 13
| [[雙五角錐]]
| 0.603005665
| <math>\frac{1}{12} \left(5+\sqrt{5}\right)</math>
|-
| 14
| [[雙三角錐柱]]
| 0.668714962
| <math>\frac{1}{12} \left(2 \sqrt{2}+3 \sqrt{3}\right)</math>
|-
| 15
| [[雙四角錐柱]]
| 1.471404521
| <math>\frac{1}{3} \left(3+\sqrt{2}\right)</math>
|-
| 16
| [[雙五角錐柱]]
| 2.323483065
| <math>\frac{1}{12} \left(5+\sqrt{5}+3 \sqrt{5 \left(5+2 \sqrt{5}\right)}\right)</math>
|-
| 17
| [[雙四角錐反角柱]]
| 1.428404503
| <math>\frac{1}{3} \left(\sqrt{2}+\sqrt{4+3 \sqrt{2}}\right)</math>
|-
| 18
| [[三角帳塔柱]]
| 3.776587513
| <math>\frac{1}{6} \left(5 \sqrt{2}+9 \sqrt{3}\right)</math>
|-
| 19
| [[四角帳塔柱]]
| 6.771236166
| <math>3+\frac{8 \sqrt{2}}{3}</math>
|-
| 20
| [[五角帳塔柱]]
| 10.018254161
| <math>\frac{1}{6} \left(5+4 \sqrt{5}+15 \sqrt{5+2 \sqrt{5}}\right)</math>
|-
| 21
| [[正五角罩帳柱]]
| 14.611971811
| <math>\frac{1}{12} \left(45+17 \sqrt{5}+30 \sqrt{5+2 \sqrt{5}}\right)</math>
|-
| 22
| [[正三角帳塔反角柱]]
| 3.516053091
| <math>\frac{1}{3} \sqrt{\frac{61}{2}+18 \sqrt{3}+30 \sqrt{1+\sqrt{3}}}</math>
|-
| 23
| [[正四角帳塔反角柱]]
| 6.210765792
| [[#23號方程|8次方程的根]]
|-
| 24
| [[正五角台塔反角柱]]
| 9.073333194
| [[#24號方程|8次方程的根]]
|-
| 25
| [[正五角罩帳反角柱]]
| 13.667050844
| [[#25號方程|8次方程的根]]
|-
| 26
| [[異相雙三角柱]]
| 0.866025404
| <math>\frac{\sqrt{3}}{2}</math>
|-
| 27
| [[同相雙三角台塔]]
| 2.357022604
| <math>\frac{5 \sqrt{2}}{3}</math>
|-
| 28
| [[同相雙四角台塔]]
| 3.885618083
| <math>2+\frac{4 \sqrt{2}}{3}</math>
|-
| 29
| [[異相雙四角台塔]]
| 3.885618083
| <math>2+\frac{4 \sqrt{2}}{3}</math>
|-
| 30
| [[同相雙五角台塔]]
| 4.648090637
| <math>\frac{1}{3} \left(5+4 \sqrt{5}\right)</math>
|-
| 31
| [[異相雙五角台塔]]
| 4.648090637
| <math>\frac{1}{3} \left(5+4 \sqrt{5}\right)</math>
|-
| 32
| [[同相五角台塔丸塔]]
| 9.241808286
| <math>\frac{5}{12} \left(11+5 \sqrt{5}\right)</math>
|-
| 33
| [[異相五角台塔丸塔]]
| 9.241808286
| <math>\frac{5}{12} \left(11+5 \sqrt{5}\right)</math>
|-
| 34
| {{link-en|同相雙五角丸塔|Pentagonal orthobirotunda}}
| 13.835525936
| <math>\frac{1}{6} \left(45+17 \sqrt{5}\right)</math>
|-
| 35
| {{link-en|同相雙三角台塔柱|Elongated triangular orthobicupola}}
| 4.955098815
| <math>\frac{5 \sqrt{2}}{3}+\frac{3 \sqrt{3}}{2}</math>
|-
| 36
| {{link-en|異相雙三角台塔柱|Elongated triangular gyrobicupola}}
| 4.955098815
| <math>\frac{5 \sqrt{2}}{3}+\frac{3 \sqrt{3}}{2}</math>
|-
| 37
| [[異相雙四角台塔柱]]
| 8.714045208
| <math>4+\frac{10 \sqrt{2}}{3}</math>
|-
| 38
| {{link-en|同相雙五角台塔柱|Elongated pentagonal orthobicupola}}
| 12.342299480
| <math>\frac{1}{6} \left(10+8 \sqrt{5}+15 \sqrt{5+2 \sqrt{5}}\right)</math>
|-
| 39
| {{link-en|異相雙五角台塔柱|Elongated pentagonal gyrobicupola}}
| 12.342299480
| <math>\frac{1}{6} \left(10+8 \sqrt{5}+15 \sqrt{5+2 \sqrt{5}}\right)</math>
|-
| 40
| {{link-en|同相五角台塔丸塔柱|Elongated pentagonal orthocupolarotunda}}
| 16.936017129
| <math>\frac{5}{12} \left(11+5 \sqrt{5}+6 \sqrt{5+2 \sqrt{5}}\right)</math>
|-
| 41
| {{link-en|異相五角台塔丸塔柱|Elongated pentagonal gyrocupolarotunda}}
| 16.936017129
| <math>\frac{5}{12} \left(11+5 \sqrt{5}+6 \sqrt{5+2 \sqrt{5}}\right)</math>
|-
| 42
| {{link-en|同相五角雙丸塔柱|Elongated pentagonal orthobirotunda}}
| 21.529734779
| <math>\frac{1}{6} \left(45+17 \sqrt{5}+15 \sqrt{5+2 \sqrt{5}}\right)</math>
|-
| 43
| {{link-en|異相五角雙丸塔柱|Elongated pentagonal gyrobirotunda}}
| 21.529734779
| <math>\frac{1}{6} \left(45+17 \sqrt{5}+15 \sqrt{5+2 \sqrt{5}}\right)</math>
|-
| 44
| {{link-en|雙三角台塔反角柱|Gyroelongated triangular bicupola}}
| 4.694564393
| <math>\frac{1}{3} \sqrt{68+18 \sqrt{3}+60 \sqrt{1+\sqrt{3}}}</math>
|-
| 45
| {{link-en|雙四角台塔反角柱|Gyroelongated square bicupola}}
| 8.153574834
| [[#45號方程|8次方程的根]]
|-
| 46
| {{link-en|雙五角台塔反角柱|Gyroelongated pentagonal bicupola}}
| 11.397378512
| [[#46號方程|8次方程的根]]
|-
| 47
| {{link-en|五角台塔丸塔反角柱|Gyroelongated pentagonal cupolarotunda}}
| 15.991096162
| [[#47號方程|8次方程的根]]
|-
| 48
| {{link-en|雙五角丸塔反角柱|Gyroelongated pentagonal birotunda}}
| 20.584813812
| [[#48號方程|8次方程的根]]
|-
| 49
| [[側錐三角柱]]
| 0.668714962
| <math>\frac{1}{12} \left(2 \sqrt{2}+3 \sqrt{3}\right)</math>
|-
| 50
| [[二側錐三角柱]]
| 0.904417223
| <math>\sqrt{\frac{59}{144}+\frac{1}{\sqrt{6}}}</math>
|-
| 51
| [[三側錐三角柱]]
| 1.140119483
| <math>\frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{4}</math>
|-
| 52
| [[側錐五角柱]]
| 1.956179661
| <math>\frac{1}{12} \sqrt{233+90 \sqrt{5}+12 \sqrt{50+20 \sqrt{5}}}</math>
|-
| 53
| [[間二側錐五角柱]]
| 2.191881921
| <math>\frac{1}{12} \sqrt{257+90 \sqrt{5}+24 \sqrt{50+20 \sqrt{5}}}</math>
|-
| 54
| [[側錐六角柱]]
| 2.833778472
| <math>\frac{1}{6} \left(\sqrt{2}+9 \sqrt{3}\right)</math>
|-
| 55
| [[對二側錐六角柱]]
| 3.069480732
| <math>\frac{1}{6} \left(2 \sqrt{2}+9 \sqrt{3}\right)</math>
|-
| 56
| [[間二側錐六角柱]]
| 3.069480732
| <math>\frac{1}{6} \left(2 \sqrt{2}+9 \sqrt{3}\right)</math>
|-
| 57
| [[三側錐六角柱]]
| 3.305182993
| <math>\frac{1}{\sqrt{2}}+\frac{3 \sqrt{3}}{2}</math>
|-
| 58
| {{link-en|侧锥正十二面体|Augmented dodecahedron}}
| 7.964621793
| <math>\frac{1}{24} \left(95+43 \sqrt{5}\right)</math>
|-
| 59
| {{link-en|对二侧锥正十二面体|Parabiaugmented dodecahedron}}
| 8.266124625
| <math>\frac{1}{6} \left(25+11 \sqrt{5}\right)</math>
|-
| 60
| {{link-en|间二侧锥正十二面体|Metabiaugmented dodecahedron}}
| 8.266124625
| <math>\frac{1}{6} \left(25+11 \sqrt{5}\right)</math>
|-
| 61
| {{link-en|三侧锥正十二面体|Triaugmented dodecahedron}}
| 8.567627458
| <math>\frac{5}{8} \left(7+3 \sqrt{5}\right)</math>
|-
| 62
| {{link-en|正二十面體欠鄰二側錐|Metabidiminished icosahedron}}
| 1.578689326
| <math>\frac{1}{6} \left(5+2 \sqrt{5}\right)</math>
|-
| 63
| {{link-en|正二十面體欠三側錐|Tridiminished icosahedron}}
| 1.277186493
| <math>\frac{5}{8}+\frac{7 \sqrt{5}}{24}</math>
|-
| 64
| {{link-en|側錐正二十面體欠三側錐|Augmented tridiminished icosahedron}}
| 1.395037624
| <math>\frac{1}{24} \left(15+2 \sqrt{2}+7 \sqrt{5}\right)</math>
|-
| 65
| [[側台塔截角四面體]]
| 3.889087297
| <math>\frac{11}{2 \sqrt{2}}</math>
|-
| 66
| [[側台塔截角立方體]]
| 15.542472333
| <math>8+\frac{16 \sqrt{2}}{3}</math>
|-
| 67
| [[對二側帳塔截角立方體]]
| 17.485281374
| <math>9+6 \sqrt{2}</math>
|-
| 68
| {{link-en|側台塔截角十二面體|Augmented truncated dodecahedron}}
| 87.363709878
| <math>\frac{505}{12}+\frac{81 \sqrt{5}}{4}</math>
|-
| 69
| {{link-en|對二側台塔截角十二面體|Parabiaugmented truncated dodecahedron}}
| 89.687755196
| <math>\frac{1}{12} \left(515+251 \sqrt{5}\right)</math>
|-
| 70
| {{link-en|間二側台塔截角十二面體|Metabiaugmented truncated dodecahedron}}
| 89.687755196
| <math>\frac{1}{12} \left(515+251 \sqrt{5}\right)</math>
|-
| 71
| {{link-en|三側台塔截角十二面體|Triaugmented truncated dodecahedron}}
| 92.011800514
| <math>\frac{7}{12} \left(75+37 \sqrt{5}\right)</math>
|-
| 72
| {{link-en|單旋側帳塔小斜方截半二十面體|Gyrate rhombicosidodecahedron}}
| 41.615323782
| <math>20+\frac{29 \sqrt{5}}{3}</math>
|-
| 73
| {{link-en|對二旋側台塔小斜方截半二十面體|Parabigyrate rhombicosidodecahedron}}
| 41.615323782
| <math>20+\frac{29 \sqrt{5}}{3}</math>
|-
| 74
| {{link-en|鄰二旋側台塔小斜方截半二十面體|Metabigyrate rhombicosidodecahedron}}
| 41.615323782
| <math>20+\frac{29 \sqrt{5}}{3}</math>
|-
| 75
| {{link-en|三旋側台塔小斜方截半二十面體|Trigyrate rhombicosidodecahedron}}
| 41.615323782
| <math>20+\frac{29 \sqrt{5}}{3}</math>
|-
| 76
| {{link-en|小斜方截半二十面體欠一側台塔|Diminished rhombicosidodecahedron}}
| 39.291278464
| <math>\frac{115}{6}+9 \sqrt{5}</math>
|-
| 77
| {{link-en|對單旋側台塔小斜方截半二十面體欠一側台塔|Paragyrate diminished rhombicosidodecahedron}}
| 39.291278464
| <math>\frac{115}{6}+9 \sqrt{5}</math>
|-
| 78
| {{link-en|鄰單旋側台塔小斜方截半二十面體欠一側台塔|Metagyrate diminished rhombicosidodecahedron}}
| 39.291278464
| <math>\frac{115}{6}+9 \sqrt{5}</math>
|-
| 79
| {{link-en|二旋側台塔小斜方截半二十面體欠一側台塔|Bigyrate diminished rhombicosidodecahedron}}
| 39.291278464
| <math>\frac{115}{6}+9 \sqrt{5}</math>
|-
| 80
| [[小斜方截半二十面體欠對二側帳塔]]
| 36.967233146
| <math>\frac{5}{3} \left(11+5 \sqrt{5}\right)</math>
|-
| 81
| {{link-en|小斜方截半二十面體欠鄰二側帳塔|Metabidiminished rhombicosidodecahedron}}
| 36.967233146
| <math>\frac{5}{3} \left(11+5 \sqrt{5}\right)</math>
|-
| 82
| [[單旋側台塔小斜方截半二十面體欠二側台塔]]
| 36.967233146
| <math>\frac{5}{3} \left(11+5 \sqrt{5}\right)</math>
|-
| 83
| [[小斜方截半二十面體欠三側台塔]]
| 34.643187827
| <math>\frac{35}{2}+\frac{23 \sqrt{5}}{3}</math>
|-
| 84
| [[扭稜鍥形體]]
| 0.859493646
| [[#84號方程|6次方程的根]]
|-
| 85
| [[扭稜四角反角柱]]
| 3.601222010
| [[#85號方程|12次方程的根]]
|-
| 86
| [[球狀屋頂]]
| 1.515351640
| <math>\frac{1}{2} \sqrt{1+3 \sqrt{\frac{3}{2}}+\sqrt{13+3 \sqrt{6}}}</math>
|-
| 87
| [[側錐球狀屋頂]]
| 1.751053900
| [[#87號方程|16次方程的根]]
|-
| 88
| [[加長型球狀屋頂]]
| 1.948108229
| [[#88號方程|32次方程的根]]
|-
| 89
| [[廣底加長型球狀屋頂]]
| 2.912910415
| [[#89號方程|20次方程的根]]
|-
| 90
| [[五角錐球狀屋頂]]
| 3.777645342
| [[#90號方程|24次方程的根]]
|-
| 91
| [[雙新月雙罩帳]]
| 3.093717650
| <math>\frac{1}{12} \left(17+9 \sqrt{5}\right)</math>
|-
| 92
| [[三角廣底球狀罩帳]]
| 5.108745974
| <math>\frac{5}{2}+\frac{7 \sqrt{5}}{6}</math>
|}

在固定邊長的條件下，[[正四角錐]]{{math|''J''<sub>1</sub>}}和[[雙三角錐]]{{math|''J''<sub>12</sub>}}的體積最小；而{{link-en|三側台塔截角十二面體|Triaugmented truncated dodecahedron}}{{math|''J''<sub>71</sub>}}的體積最大，比前者大超過390倍。

在92種詹森多面體中，有13種詹森多面體的體積{{math|''V''/''a''<sup>3</sup>}}無法表達為[[解析解|解析數]]。這些數值是以下多項式的最大實根。

{| class="wikitable sortable"
|-
! {{math|''J''<sub>''n''</sub>}}
! 多項式
|-
| {{vanchor|23號方程|text=23}}
| 
{{math|
6561 ''x''<sup>8</sup>
&minus; 52488 ''x''<sup>7</sup>
+ 113724 ''x''<sup>6</sup>
&minus; 9720 ''x''<sup>5</sup>
<br>
&minus; 1616922 ''x''<sup>4</sup>
+ 396360 ''x''<sup>3</sup>
+ 1537020 ''x''<sup>2</sup>
&minus; 178632 ''x''
&minus; 3391}}
|-
| {{vanchor|24號方程|text=24}}
| 
{{math|
1679616 ''x''<sup>8</sup>
&minus; 11197440 ''x''<sup>7</sup>
+ 27060480 ''x''<sup>6</sup>
+ 35769600 ''x''<sup>5</sup>
<br>
&minus; 4456749600 ''x''<sup>4</sup>
&minus; 10714248000 ''x''<sup>3</sup>
+ 3828402000 ''x''<sup>2</sup>
+ 13859430000 ''x''
+ 5340175625}}
|-
| {{vanchor|25號方程|text=25}}
| 
{{math|
1679616 ''x''<sup>8</sup>
&minus; 50388480 ''x''<sup>7</sup>
+ 603262080 ''x''<sup>6</sup>
&minus; 3520972800 ''x''<sup>5</sup>
<br>
+ 5215460400 ''x''<sup>4</sup>
+ 4128624000 ''x''<sup>3</sup>
&minus; 8894943000 ''x''<sup>2</sup>
+ 3881385000 ''x''
&minus; 424924375}}
|-
| {{vanchor|45號方程|text=45}}
| 
{{math|
6561 ''x''<sup>8</sup>
&minus; 104976 ''x''<sup>7</sup>
+ 594864 ''x''<sup>6</sup>
&minus; 1384128 ''x''<sup>5</sup>
<br>
&minus; 552096 ''x''<sup>4</sup>
+ 1569024 ''x''<sup>3</sup>
+ 246528 ''x''<sup>2</sup>
&minus; 119808 ''x''
+ 4352}}
|-
| {{vanchor|46號方程|text=46}}
| 
{{math|
6561 ''x''<sup>8</sup>
&minus; 87480 ''x''<sup>7</sup>
+ 313470 ''x''<sup>6</sup>
+ 753300 ''x''<sup>5</sup>
<br>
&minus; 22424850 ''x''<sup>4</sup>
&minus; 84591000 ''x''<sup>3</sup>
&minus; 85909500 ''x''<sup>2</sup>
+ 8715000 ''x''
+ 35547500}}
|-
| {{vanchor|47號方程|text=47}}
| 
{{math|
1679616 ''x''<sup>8</sup>
&minus; 61585920 ''x''<sup>7</sup>
+ 851472000 ''x''<sup>6</sup>
&minus; 5108832000 ''x''<sup>5</sup>
<br>
+ 4745790000 ''x''<sup>4</sup>
+ 21346200000 ''x''<sup>3</sup>
&minus; 29019375000 ''x''<sup>2</sup>
&minus; 4576875000 ''x''
&minus; 405859375}}
|-
| {{vanchor|48號方程|text=48}}
| 
{{math|
6561 ''x''<sup>8</sup>
&minus; 393660 ''x''<sup>7</sup>
+ 9316620 ''x''<sup>6</sup>
&minus; 108207900 ''x''<sup>5</sup>
<br>
+ 601832025 ''x''<sup>4</sup>
&minus; 1417189500 ''x''<sup>3</sup>
+ 965841750 ''x''<sup>2</sup>
+ 597667500 ''x''
&minus; 668786875}}
|-
| {{vanchor|84號方程|text=84}}
| 
{{math|
5832 ''x''<sup>6</sup>
&minus; 1377 ''x''<sup>4</sup>
&minus; 2160 ''x''<sup>2</sup>
&minus; 4}}
|-
| {{vanchor|85號方程|text=85}}
| 
{{math|
531441 ''x''<sup>12</sup>
&minus; 85726026 ''x''<sup>8</sup>
&minus; 48347280 ''x''<sup>6</sup>
<br>
+ 11588832 ''x''<sup>4</sup>
+ 4759488 ''x''<sup>2</sup>
&minus; 892448}}
|-
| {{vanchor|87號方程|text=87}}
| 
{{math|
45137758519296 ''x''<sup>16</sup>
&minus; 110336743047168 ''x''<sup>14</sup>
&minus; 191069246324736 ''x''<sup>12</sup>
+ 209269081571328 ''x''<sup>10</sup>
<br>
+ 364547659290624 ''x''<sup>8</sup>
&minus; 58793017190400 ''x''<sup>6</sup>
+ 3306865979520 ''x''<sup>4</sup>
&minus; 1275399855936 ''x''<sup>2</sup>
+ 1439671249}}
|-
| {{vanchor|88號方程|text=88}}
| 
{{math|
521578814501447328359509917696 ''x''<sup>32</sup>
&minus; 985204427391622731345740955648 ''x''<sup>30</sup>
<br>
&minus; 16645447351681991898880656015360 ''x''<sup>28</sup>
+ 79710816694053483249372512649216 ''x''<sup>26</sup>
<br>
&minus; 152195045391070538203422101864448 ''x''<sup>24</sup>
+ 156280253448056209478031589244928 ''x''<sup>22</sup>
<br>
&minus; 96188116617075838858708654227456 ''x''<sup>20</sup>
+ 30636368373570166303441645731840 ''x''<sup>18</sup>
<br>
+ 5828527077458909552923002273792 ''x''<sup>16</sup>
&minus; 8060049780765551057159394951168 ''x''<sup>14</sup>
<br>
+ 1018074792115156107372011716608 ''x''<sup>12</sup>
+ 35220131544370794950945931264 ''x''<sup>10</sup>
<br>
+ 327511698517355918956755959808 ''x''<sup>8</sup>
&minus; 116978732884218191486738706432 ''x''<sup>6</sup>
<br>
+ 10231563774949176791703149568 ''x''<sup>4</sup>
&minus; 366323949299263261553952192 ''x''<sup>2</sup>
<br>
+ 3071435678740442112675625}}
|-
| {{vanchor|89號方程|text=89}}
| 
{{math|
47330370277129322496 ''x''<sup>20</sup>
&minus; 722445512980071186432 ''x''<sup>18</sup>
<br>
+ 3596480447590271287296 ''x''<sup>16</sup>
&minus; 8432333285523990773760 ''x''<sup>14</sup>
<br>
+ 8973584611317745975296 ''x''<sup>12</sup>
&minus; 3065290664181478981632 ''x''<sup>10</sup>
<br>
+ 366229890219212144640 ''x''<sup>8</sup>
&minus; 8337259437908852736 ''x''<sup>6</sup>
<br>
&minus; 22211277300912896 ''x''<sup>4</sup>
+ 132615435213216 ''x''<sup>2</sup>
<br>
+ 2693461945329}}
|- 
| {{vanchor|90號方程|text=90}}
| 
{{math|
1213025622610333925376 ''x''<sup>24</sup>
+ 54451372392730545094656 ''x''<sup>22</sup>
<br>
&minus; 796837093078664749252608 ''x''<sup>20</sup>
&minus; 4133410366404688544268288 ''x''<sup>18</sup>
<br>
+ 20902529024429842816303104 ''x''<sup>16</sup>
&minus; 133907540390420673677230080 ''x''<sup>14</sup>
<br>
+ 246234688242991598853881856 ''x''<sup>12</sup>
&minus; 63327534106871321714442240 ''x''<sup>10</sup>
<br>
+ 14389309497459555704164608 ''x''<sup>8</sup>
+ 48042947402464500749392128 ''x''<sup>6</sup>
<br>
&minus; 5891096640600351061013664 ''x''<sup>4</sup>
&minus; 3212114716816853362953264 ''x''<sup>2</sup>
+ 479556973248657693884401}}
|}

== 內切球半徑、中分球半徑和外接球半徑 ==
下表列出了存在內切球、中分球和外接球之詹森多面體的各種球半徑（內切球半徑{{math|''R''<sub>i</sub>}}、[[中分球]]半徑{{math|''R''<sub>m</sub>}}或外接球半徑{{math|''R''<sub>c</sub>}}，不存在則不列出）與邊長之比。

詹森多面體不一定有內切球、中分球和外接球。比方說，除非該詹森多面體的所有頂點都位於某個球面上，否則這個詹森多面體不會存在外接球。詹森多面體的對稱性比[[正多面體]]低，因此很多詹森多面體不存在這些球體。只有[[正四角錐]]{{math|''J''<sub>1</sub>}}和[[正五角錐]]{{math|''J''<sub>2</sub>}}這兩個立體三種球都存在。

表格內容的資料來源是來自[[沃尔夫勒姆研究公司]]的[[Mathematica]]軟體提供的'''<syntaxhighlight lang=mathematica inline>PolyhedronData[..., "Inradius"]</syntaxhighlight>'''、 '''<syntaxhighlight lang=mathematica inline>PolyhedronData[..., "Midradius"]</syntaxhighlight>'''和 '''<syntaxhighlight lang=mathematica inline>PolyhedronData[..., "Circumradius"]</syntaxhighlight>'''指令。 輸出的數值已被化簡過了。
{| class="wikitable sortable"
|-
! {{math|''J''<sub>''n''</sub>}}
! {{math|''R''<sub>i</sub>/a}} （近似值）
! {{math|''R''<sub>i</sub>/a}} （精確值）
! {{math|''R''<sub>m</sub>/a}} （近似值）
! {{math|''R''<sub>m</sub>/a}} （精確值）
! {{math|''R''<sub>c</sub>/a}} （近似值）
! {{math|''R''<sub>c</sub>/a}} （精確值）
|-
| 1
| 0.258819045
| <math>\frac{\sqrt{2-\sqrt{3}}}{2}</math>
| 0.500000000
| <math>\frac{1}{2}</math>
| 0.707106781
| <math>\frac{1}{\sqrt{2}}</math>
|-
| 2
| 0.232788309
| <math>\frac{1}{\sqrt{25-7 \sqrt{5}+\sqrt{30 \left(5-\sqrt{5}\right)}}}</math>
| 0.809016994
| <math>\frac{1}{4} \left(1+\sqrt{5}\right)</math>
| 0.951056516
| <math>\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}</math>
|-
| 3
| -
| -
| 0.866025404
| <math>\frac{\sqrt{3}}{2}</math>
| 1.000000000
| <math>1</math>
|-
| 4
| -
| -
| 1.306562965
| <math>\sqrt{1+\frac{1}{\sqrt{2}}}</math>
| 1.398966326
| <math>\sqrt{\frac{5}{4}+\frac{1}{\sqrt{2}}}</math>
|-
| 5
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 6
| -
| -
| 1.538841769
| <math>\frac{1}{2} \sqrt{5+2 \sqrt{5}}</math>
| 1.618033989
| <math>\frac{1}{2} \left(1+\sqrt{5}\right)</math>
|-
| 7
| -
| -
| -
| -
| -
| -
|-
| 8
| -
| -
| -
| -
| -
| -
|-
| 9
| -
| -
| -
| -
| -
| -
|-
| 10
| -
| -
| -
| -
| -
| -
|-
| 11
| -
| -
| 0.809016994
| <math>\frac{1}{4} \left(1+\sqrt{5}\right)</math>
| 0.951056516
| <math>\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}</math>
|-
| 12
| 0.272165527
| <math>\frac{\sqrt{\frac{2}{3}}}{3}</math>
| -
| -
| -
| -
|-
| 13
| 0.417774579
| <math>\sqrt{\frac{1}{30} \left(3+\sqrt{5}\right)}</math>
| -
| -
| -
| -
|-
| 14
| -
| -
| -
| -
| -
| -
|-
| 15
| -
| -
| -
| -
| -
| -
|-
| 16
| -
| -
| -
| -
| -
| -
|-
| 17
| -
| -
| -
| -
| -
| -
|-
| 18
| -
| -
| -
| -
| -
| -
|-
| 19
| -
| -
| 1.306562965
| <math>\sqrt{1+\frac{1}{\sqrt{2}}}</math>
| 1.398966326
| <math>\sqrt{\frac{5}{4}+\frac{1}{\sqrt{2}}}</math>
|-
| 20
| -
| -
| -
| -
| -
| -
|-
| 21
| -
| -
| -
| -
| -
| -
|-
| 22
| -
| -
| -
| -
| -
| -
|-
| 23
| -
| -
| -
| -
| -
| -
|-
| 24
| -
| -
| -
| -
| -
| -
|-
| 25
| -
| -
| -
| -
| -
| -
|-
| 26
| -
| -
| -
| -
| -
| -
|-
| 27
| -
| -
| 0.866025404
| <math>\frac{\sqrt{3}}{2}</math>
| 1.000000000
| <math>1</math>
|-
| 28
| -
| -
| -
| -
| -
| -
|-
| 29
| -
| -
| -
| -
| -
| -
|-
| 30
| -
| -
| -
| -
| -
| -
|-
| 31
| -
| -
| -
| -
| -
| -
|-
| 32
| -
| -
| -
| -
| -
| -
|-
| 33
| -
| -
| -
| -
| -
| -
|-
| 34
| -
| -
| 1.538841769
| <math>\frac{1}{2} \sqrt{5+2 \sqrt{5}}</math>
| 1.618033989
| <math>\frac{1}{2} \left(1+\sqrt{5}\right)</math>
|-
| 35
| -
| -
| -
| -
| -
| -
|-
| 36
| -
| -
| -
| -
| -
| -
|-
| 37
| -
| -
| 1.306562965
| <math>\sqrt{1+\frac{1}{\sqrt{2}}}</math>
| 1.398966326
| <math>\sqrt{\frac{5}{4}+\frac{1}{\sqrt{2}}}</math>
|-
| 38
| -
| -
| -
| -
| -
| -
|-
| 39
| -
| -
| -
| -
| -
| -
|-
| 40
| -
| -
| -
| -
| -
| -
|-
| 41
| -
| -
| -
| -
| -
| -
|-
| 42
| -
| -
| -
| -
| -
| -
|-
| 43
| -
| -
| -
| -
| -
| -
|-
| 44
| -
| -
| -
| -
| -
| -
|-
| 45
| -
| -
| -
| -
| -
| -
|-
| 46
| -
| -
| -
| -
| -
| -
|-
| 47
| -
| -
| -
| -
| -
| -
|-
| 48
| -
| -
| -
| -
| -
| -
|-
| 49
| -
| -
| -
| -
| -
| -
|-
| 50
| -
| -
| -
| -
| -
| -
|-
| 51
| -
| -
| -
| -
| -
| -
|-
| 52
| -
| -
| -
| -
| -
| -
|-
| 53
| -
| -
| -
| -
| -
| -
|-
| 54
| -
| -
| -
| -
| -
| -
|-
| 55
| -
| -
| -
| -
| -
| -
|-
| 56
| -
| -
| -
| -
| -
| -
|-
| 57
| -
| -
| -
| -
| -
| -
|-
| 58
| -
| -
| -
| -
| -
| -
|-
| 59
| -
| -
| -
| -
| -
| -
|-
| 60
| -
| -
| -
| -
| -
| -
|-
| 61
| -
| -
| -
| -
| -
| -
|-
| 62
| -
| -
| 0.809016994
| <math>\frac{1}{4} \left(1+\sqrt{5}\right)</math>
| 0.951056516
| <math>\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}</math>
|-
| 63
| -
| -
| 0.809016994
| <math>\frac{1}{4} \left(1+\sqrt{5}\right)</math>
| 0.951056516
| <math>\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}</math>
|-
| 64
| -
| -
| -
| -
| -
| -
|-
| 65
| -
| -
| -
| -
| -
| -
|-
| 66
| -
| -
| -
| -
| -
| -
|-
| 67
| -
| -
| -
| -
| -
| -
|-
| 68
| -
| -
| -
| -
| -
| -
|-
| 69
| -
| -
| -
| -
| -
| -
|-
| 70
| -
| -
| -
| -
| -
| -
|-
| 71
| -
| -
| -
| -
| -
| -
|-
| 72
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 73
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 74
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 75
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 76
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 77
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 78
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 79
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 80
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 81
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 82
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 83
| -
| -
| 2.176250899
| <math>\sqrt{\frac{5}{2}+\sqrt{5}}</math>
| 2.232950509
| <math>\frac{1}{2} \sqrt{11+4 \sqrt{5}}</math>
|-
| 84
| -
| -
| -
| -
| -
| -
|-
| 85
| -
| -
| -
| -
| -
| -
|-
| 86
| -
| -
| -
| -
| -
| -
|-
| 87
| -
| -
| -
| -
| -
| -
|-
| 88
| -
| -
| -
| -
| -
| -
|-
| 89
| -
| -
| -
| -
| -
| -
|-
| 90
| -
| -
| -
| -
| -
| -
|-
| 91
| -
| -
| -
| -
| -
| -
|-
| 92
| -
| -
| -
| -
| -
| -
|}

== 參見 ==
*[[詹森多面體]]

== 參考文獻 ==
{{Reflist}}

== 外部連結 ==
* Sylvain Gagnon, "[http://haydn.upc.es/people/ros/StructuralTopology/ST6/st6-11-a7-ocr.pdf Convex polyhedra with regular faces]{{dead link|date=December 2017 |bot=InternetArchiveBot |fix-attempted=yes }}", Structural Topology, No. 6, 1982, 83-95.
* [http://www.georgehart.com/virtual-polyhedra/johnson-info.html Johnson Solids] {{Wayback|url=http://www.georgehart.com/virtual-polyhedra/johnson-info.html |date=20220111070112 }} by George W. Hart.
* [https://web.archive.org/web/20130601082835/http://www.uwgb.edu/dutchs/symmetry/johnsonp.htm Images of all 92 solids, categorized, on one page]
* {{MathWorld | urlname=JohnsonSolid | title=Johnson Solid}}
* [http://www.orchidpalms.com/polyhedra/johnson/johnson.html VRML models of Johnson Solids] {{Wayback|url=http://www.orchidpalms.com/polyhedra/johnson/johnson.html |date=20231113060748 }} by Jim McNeill
* [http://bulatov.org/polyhedra/johnson/ VRML models of Johnson Solids] {{Wayback|url=http://bulatov.org/polyhedra/johnson/ |date=20070928011621 }} by Vladimir Bulatov

{{詹森多面體}}

[[Category:约翰逊多面体]]