ジョンソンの立体
一覧

番号と英語の名称はジョンソンによる。日本語訳にはいくらか揺れがあるので注意されたい。n 番目のジョンソンの立体を Jn と書く。
1-6（6種）: 角錐、台塔、丸塔
7-17（11種）: 角錐柱、角錐反柱、双角錐
18-48（31種）: 台塔と丸塔の変形
49-57（9種）: 側錐角柱
58-64（7種）: 正多面体の変形
65-83（19種）: 半正多面体の変形
84-92（9種）: その他
対称性はシェーンフリース記号で書かれている。ほかの記号法についてはList of spherical symmetry groups（3次元点群の一覧）に詳しい。
| Jn | 名称 | 展開図 | 投影図 | 頂 点 | 辺 | 面 | 正 n 角形面> 3 | 正 n 角形面> 4 | 正 n 角形面> 5 | 正 n 角形面> 6 | 正 n 角形面> 8 | 正 n 角形面> 10 | 対 称 性 | その他の 性質 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | 正四角錐 (square pyramid) |  |  | 5 | 8 | 5 | 4 | 1 |  |  |  |  | C4v |  |
| 2 | 正五角錐 (pentagonal pyramid) |  |  | 6 | 10 | 6 | 5 |  | 1 |  |  |  | C5v |  |
| 3 | 正三角台塔 (triangular cupola) |  |  | 9 | 15 | 8 | 4 | 3 |  | 1 |  |  | C3v |  |
| 4 | 正四角台塔 (square cupola) |  |  | 12 | 20 | 10 | 4 | 5 |  |  | 1 |  | C4v |  |
| 5 | 正五角台塔 (pentagonal cupola) |  |  | 15 | 25 | 12 | 5 | 5 | 1 |  |  | 1 | C5v |  |
| 6 | 正五角丸塔 (pentagonal rotunda) |  |  | 20 | 35 | 17 | 10 |  | 6 |  |  | 1 | C5v |  |
| 7 | 正三角錐柱 (elongated triangular pyramid) |  |  | 7 | 12 | 7 | 4 | 3 |  |  |  |  | C3v |  |
| 8 | 正四角錐柱 (elongated square pyramid) |  |  | 9 | 16 | 9 | 4 | 5 |  |  |  |  | C4v |  |
| 9 | 正五角錐柱 (elongated pentagonal pyramid) |  |  | 11 | 20 | 11 | 5 | 5 | 1 |  |  |  | C5v |  |
| 10 | 正四角錐反柱 (gyroelongated square pyramid) |  |  | 9 | 20 | 13 | 12 | 1 |  |  |  |  | C4v |  |
| 11 | 正五角錐反柱 (gyroelongated pentagonal pyramid) |  |  | 11 | 25 | 16 | 15 |  | 1 |  |  |  | C5v |  |
| 12 | 双三角錐 (triangular dipyramid) デルタ六面体 |  |  | 5 | 9 | 6 | 6 |  |  |  |  |  | D3h | デルタ 多面体 |
| 13 | 双五角錐 (pentagonal dipyramid) デルタ十面体 |  |  | 7 | 15 | 10 | 10 |  |  |  |  |  | D5h | デルタ 多面体 |
| 14 | 双三角錐柱 (elongated triangular dipyramid) |  |  | 8 | 15 | 9 | 6 | 3 |  |  |  |  | D3h |  |
| 15 | 双四角錐柱 (elongated square dipyramid) |  |  | 10 | 20 | 12 | 8 | 4 |  |  |  |  | D4h |  |
| 16 | 双五角錐柱 (elongated pentagonal dipyramid) |  |  | 12 | 25 | 15 | 10 | 5 |  |  |  |  | D5h |  |
| 17 | 双四角錐反柱 (gyroelongated square dipyramid) デルタ十六面体 |  |  | 10 | 24 | 16 | 16 |  |  |  |  |  | D4d | デルタ 多面体 |
| 18 | 正三角台塔柱 (elongated triangular cupola) |  |  | 15 | 27 | 14 | 4 | 9 |  | 1 |  |  | C3v |  |
| 19 | 正四角台塔柱 (elongated square cupola) |  |  | 20 | 36 | 18 | 4 | 13 |  |  | 1 |  | C4v |  |
| 20 | 正五角台塔柱 (elongated pentagonal cupola) |  |  | 25 | 45 | 22 | 5 | 15 | 1 |  |  | 1 | C5v |  |
| 21 | 正五角丸塔柱 (elongated pentagonal rotunda) |  |  | 30 | 55 | 27 | 10 | 10 | 6 |  |  | 1 | C5v |  |
| 22 | 正三角台塔反柱 (gyroelongated triangular cupola) |  |  | 15 | 33 | 20 | 16 | 3 |  | 1 |  |  | C3v |  |
| 23 | 正四角台塔反柱 (gyroelongated square cupola) |  |  | 20 | 44 | 26 | 20 | 5 |  |  | 1 |  | C4v |  |
| 24 | 正五角台塔反柱 (gyroelongated pentagonal cupola) |  |  | 25 | 55 | 32 | 25 | 5 | 1 |  |  | 1 | C5v |  |
| 25 | 正五角丸塔反柱 (gyroelongated pentagonal rotunda) |  |  | 30 | 65 | 37 | 30 |  | 6 |  |  | 1 | C5v |  |
| 26 | 異相双三角柱 (gyrobifastigium) 双側正三角柱 |  |  | 8 | 14 | 8 | 4 | 4 |  |  |  |  | D2d |  |
| 27 | 同相双三角台塔 (triangular orthobicupola) |  |  | 12 | 24 | 14 | 8 | 6 |  |  |  |  | D3h |  |
| 28 | 同相双四角台塔 (square orthobicupola) |  |  | 16 | 32 | 18 | 8 | 10 |  |  |  |  | D4h |  |
| 29 | 異相双四角台塔 (square gyrobicupola) |  |  | 16 | 32 | 18 | 8 | 10 |  |  |  |  | D4d |  |
| 30 | 同相双五角台塔 (pentagonal orthobicupola) |  |  | 20 | 40 | 22 | 10 | 10 | 2 |  |  |  | D5h |  |
| 31 | 異相双五角台塔 (pentagonal gyrobicupola) |  |  | 20 | 40 | 22 | 10 | 10 | 2 |  |  |  | D5d |  |
| 32 | 同相五角台塔丸塔 (pentagonal orthocupolarotunda) |  |  | 25 | 50 | 27 | 15 | 5 | 7 |  |  |  | C5v |  |
| 33 | 異相五角台塔丸塔 (pentagonal gyrocupolarotunda) |  |  | 25 | 50 | 27 | 15 | 5 | 7 |  |  |  | C5v |  |
| 34 | 同相双五角丸塔 (pentagonal orthobirotunda) |  |  | 30 | 60 | 32 | 20 |  | 12 |  |  |  | D5h |  |
| 35 | 同相双三角台塔柱 (elongated triangular orthobicupola) |  |  | 18 | 36 | 20 | 8 | 12 |  |  |  |  | D3h |  |
| 36 | 異相双三角台塔柱 (elongated triangular gyrobicupola) |  |  | 18 | 36 | 20 | 8 | 12 |  |  |  |  | D3d |  |
| 37 | 異相双四角台塔柱 (elongated square gyrobicupola) ミラーの立体 |  |  | 24 | 48 | 26 | 8 | 18 |  |  |  |  | D4d | 全ての 頂点形状 が合同 |
| 38 | 同相双五角台塔柱 (elongated pentagonal orthobicupola) |  |  | 30 | 60 | 32 | 10 | 20 | 2 |  |  |  | D5h |  |
| 39 | 異相双五角台塔柱 (elongated pentagonal gyrobicupola) |  |  | 30 | 60 | 32 | 10 | 20 | 2 |  |  |  | D5d |  |
| 40 | 同相五角台塔丸塔柱 (elongated pentagonal orthocupolarotunda) |  |  | 35 | 70 | 37 | 15 | 15 | 7 |  |  |  | C5v |  |
| 41 | 異相五角台塔丸塔柱 (elongated pentagonal gyrocupolarotunda) |  |  | 35 | 70 | 37 | 15 | 15 | 7 |  |  |  | C5v |  |
| 42 | 同相双五角丸塔柱 (elongated pentagonal orthobirotunda) |  |  | 40 | 80 | 42 | 20 | 10 | 12 |  |  |  | D5h |  |
| 43 | 異相双五角丸塔柱 (elongated pentagonal gyrobirotunda) |  |  | 40 | 80 | 42 | 20 | 10 | 12 |  |  |  | D5d |  |
| 44 | 双三角台塔反柱 (gyroelongated triangular bicupola) |  |  | 18 | 42 | 26 | 20 | 6 |  |  |  |  | D3 | キラル |
| 45 | 双四角台塔反柱 (gyroelongated square bicupola) |  |  | 24 | 56 | 34 | 24 | 10 |  |  |  |  | D4 | キラル |
| 46 | 双五角台塔反柱 (gyroelongated pentagonal bicupola) |  |  | 30 | 70 | 42 | 30 | 10 | 2 |  |  |  | D5 | キラル |
| 47 | 五角台塔丸塔反柱 (gyroelongated pentagonal cupolarotunda) |  |  | 35 | 80 | 47 | 35 | 5 | 7 |  |  |  | C5 | キラル |
| 48 | 双五角丸塔反柱 (gyroelongated pentagonal birotunda) |  |  | 40 | 90 | 52 | 40 |  | 12 |  |  |  | D5 | キラル |
| 49 | 側錐三角柱 (augmented triangular prism) |  |  | 7 | 13 | 8 | 6 | 2 |  |  |  |  | C2v |  |
| 50 | 二側錐三角柱 (biaugmented triangular prism) |  |  | 8 | 17 | 11 | 10 | 1 |  |  |  |  | C2v |  |
| 51 | 三側錐三角柱 (triaugmented triangular prism) デルタ十四面体 |  |  | 9 | 21 | 14 | 14 |  |  |  |  |  | D3h | デルタ 多面体 |
| 52 | 側錐五角柱 (augmented pentagonal prism) |  |  | 11 | 19 | 10 | 4 | 4 | 2 |  |  |  | C2v |  |
| 53 | 二側錐五角柱 (biaugmented pentagonal prism) |  |  | 12 | 23 | 13 | 8 | 3 | 2 |  |  |  | C2v |  |
| 54 | 側錐六角柱 (augmented hexagonal prism) |  |  | 13 | 22 | 11 | 4 | 5 |  | 2 |  |  | C2v |  |
| 55 | 双側錐六角柱 (parabiaugmented hexagonal prism) |  |  | 14 | 26 | 14 | 8 | 4 |  | 2 |  |  | D2h |  |
| 56 | 二側錐六角柱 (metabiaugmented hexagonal prism) |  |  | 14 | 26 | 14 | 8 | 4 |  | 2 |  |  | C2v |  |
| 57 | 三側錐六角柱 (triaugmented hexagonal prism) |  |  | 15 | 30 | 17 | 12 | 3 |  | 2 |  |  | D3h |  |
| 58 | 側錐十二面体 (augmented dodecahedron) |  |  | 21 | 35 | 16 | 5 |  | 11 |  |  |  | C5v |  |
| 59 | 双側錐十二面体 (parabiaugmented dodecahedron) |  |  | 22 | 40 | 20 | 10 |  | 10 |  |  |  | D5d |  |
| 60 | 二側錐十二面体 (metabiaugmented dodecahedron) |  |  | 22 | 40 | 20 | 10 |  | 10 |  |  |  | C2v |  |
| 61 | 三側錐十二面体 (triaugmented dodecahedron) |  |  | 23 | 45 | 24 | 15 |  | 9 |  |  |  | C3v |  |
| 62 | 二側錐欠損二十面体 (metabidiminished icosahedron) |  |  | 10 | 20 | 12 | 10 |  | 2 |  |  |  | C2v |  |
| 63 | 三側錐欠損二十面体 (tridiminished icosahedron) |  |  | 9 | 15 | 8 | 5 |  | 3 |  |  |  | C3v |  |
| 64 | 側錐三側錐欠損二十面体 (augmented tridiminished icosahedron) |  |  | 10 | 18 | 10 | 7 |  | 3 |  |  |  | C3v |  |
| 65 | 側台塔切頂四面体 (augmented truncated tetrahedron) |  |  | 15 | 27 | 14 | 8 | 3 |  | 3 |  |  | C3v |  |
| 66 | 側台塔切頂立方体 (augmented truncated cube) |  |  | 28 | 48 | 22 | 12 | 5 |  |  | 5 |  | C4v |  |
| 67 | 双側台塔切頂立方体 (biaugmented truncated cube) |  |  | 32 | 60 | 30 | 16 | 10 |  |  | 4 |  | D4h |  |
| 68 | 側台塔切頂十二面体 (augmented truncated dodecahedron) |  |  | 65 | 105 | 42 | 25 | 5 | 1 |  |  | 11 | C5v |  |
| 69 | 双側台塔切頂十二面体 (parabiaugmented truncated dodecahedron) |  |  | 70 | 120 | 52 | 30 | 10 | 2 |  |  | 10 | D5d |  |
| 70 | 二側台塔切頂十二面体 (metabiaugmented truncated dodecahedron) |  |  | 70 | 120 | 52 | 30 | 10 | 2 |  |  | 10 | C2v |  |
| 71 | 三側台塔切頂十二面体 (triaugmented truncated dodecahedron) |  |  | 75 | 135 | 62 | 35 | 15 | 3 |  |  | 9 | C3v |  |
| 72 | 側台塔回転斜方二十・十二面体 (gyrate rhombicosidodecahedron) |  |  | 60 | 120 | 62 | 20 | 30 | 12 |  |  |  | C5v |  |
| 73 | 双側台塔回転斜方二十・十二面体 (parabigyrate rhombicosidodecahedron) |  |  | 60 | 120 | 62 | 20 | 30 | 12 |  |  |  | D5d |  |
| 74 | 二側台塔回転斜方二十・十二面体 (metabigyrate rhombicosidodecahedron) |  |  | 60 | 120 | 62 | 20 | 30 | 12 |  |  |  | C2v |  |
| 75 | 三側台塔回転斜方二十・十二面体 (trigyrate rhombicosidodecahedron) |  |  | 60 | 120 | 62 | 20 | 30 | 12 |  |  |  | C3v |  |
| 76 | 側台塔欠損斜方二十・十二面体 (diminished rhombicosidodecahedron) |  |  | 55 | 105 | 52 | 15 | 25 | 11 |  |  | 1 | C5v |  |
| 77 | 双側台塔回転欠損斜方二十・十二面体 (paragyrate diminished rhombicosidodecahedron) |  |  | 55 | 105 | 52 | 15 | 25 | 11 |  |  | 1 | C5v |  |
| 78 | 二側台塔回転欠損斜方二十・十二面体 (metagyrate diminished rhombicosidodecahedron) |  |  | 55 | 105 | 52 | 15 | 25 | 11 |  |  | 1 | Cs |  |
| 79 | 二側台塔回転側台塔欠損斜方二十・十二面体 (bigyrate diminished rhombicosidodecahedron) |  |  | 55 | 105 | 52 | 15 | 25 | 11 |  |  | 1 | Cs |  |
| 80 | 双側台塔欠損斜方二十・十二面体 (parabidiminished rhombicosidodecahedron) |  |  | 50 | 90 | 42 | 10 | 20 | 10 |  |  | 2 | D5d |  |
| 81 | 二側台塔欠損斜方二十・十二面体 (metabidiminished rhombicosidodecahedron) |  |  | 50 | 90 | 42 | 10 | 20 | 10 |  |  | 2 | C2v |  |
| 82 | 側台塔回転二側台塔欠損斜方二十・十二面体 (gyrate bidiminished rhombicosidodecahedron) |  |  | 50 | 90 | 42 | 10 | 20 | 10 |  |  | 2 | Cs |  |
| 83 | 三側台塔欠損斜方二十・十二面体 (tridiminished rhombicosidodecahedron) |  |  | 45 | 75 | 32 | 5 | 15 | 9 |  |  | 3 | C3v |  |
| 84 | 変形双五角錐 (snub disphenoid) デルタ十二面体 |  |  | 8 | 18 | 12 | 12 |  |  |  |  |  | D2d | デルタ 多面体 |
| 85 | 変形四角反柱 (snub square antiprism) |  |  | 16 | 40 | 26 | 24 | 2 |  |  |  |  | D4d |  |
| 86 | 球形屋根 (sphenocorona) |  |  | 10 | 22 | 14 | 12 | 2 |  |  |  |  | C2v |  |
| 87 | 側錐球形屋根 (augmented sphenocorona) |  |  | 11 | 26 | 17 | 16 | 1 |  |  |  |  | Cs |  |
| 88 | 長球形屋根 (sphenomegacorona) |  |  | 12 | 28 | 18 | 16 | 2 |  |  |  |  | C2v |  |
| 89 | 広底長球形屋根 (hebesphenomegacorona) |  |  | 14 | 33 | 21 | 18 | 3 |  |  |  |  | C2v |  |
| 90 | 五角錐球形屋根 (disphenocingulum) |  |  | 16 | 38 | 24 | 20 | 4 |  |  |  |  | D2d |  |
| 91 | 双三日月双丸塔 (bilunabirotunda) |  |  | 14 | 26 | 14 | 8 | 2 | 4 |  |  |  | D2h |  |
| 92 | 三角広底球形屋根丸塔 (triangular hebesphenorotunda) |  |  | 18 | 36 | 20 | 13 | 3 | 3 | 1 |  |  | C3v |  |