قائمة مجسمات جونسون

| 48 | Gyroelongated pentagonal birotunda |  | 40 | 90 | 52 |  D_{5} من الرتبة 10 |  {\begin{aligned}A&=\left(10{\sqrt {3}}+3{\sqrt {25+10{\sqrt {5}}}}\right)a^{2}\\&\approx 37.9662a^{2}\\V&=\left({\frac {45}{6}}+{\frac {17}{6}}{\sqrt {5}}+{\frac {5}{6}}{\sqrt {2{\sqrt {650+290{\sqrt {5}}}}-2{\sqrt {5}}-2}}\right)a^{3}\\&\approx 20.5848a^{3}\end{aligned}} |
| 49 | Augmented triangular prism |  | 7 | 13 | 8 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&={\frac {1}{2}}(4+3{\sqrt {3}})a^{2}\\&\approx 4.5981a^{2}\\V&={\frac {1}{12}}(2{\sqrt {2}}+3{\sqrt {3}})a^{3}\\&\approx 0.6687a^{3}\end{aligned}} |
| 50 | Biaugmented triangular prism |  | 8 | 17 | 11 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&={\frac {1}{2}}(2+5{\sqrt {3}})a^{2}\\&\approx 5.3301a^{2}\\V&={\sqrt {{\frac {59}{144}}+{\frac {1}{\sqrt {6}}}}}a^{3}\\&\approx 0.9044a^{3}\end{aligned}} |
| 51 | Triaugmented triangular prism |  | 9 | 21 | 14 |  D_{3h} من الرتبة 12 |  {\begin{aligned}A&={\frac {7{\sqrt {3}}}{2}}a^{2}\\&\approx 6.0622a^{2}\\V&={\frac {2{\sqrt {2}}+{\sqrt {3}}}{4}}a^{3}\\&\approx 1.1401a^{3}\end{aligned}} |
| 52 | Augmented pentagonal prism |  | 11 | 19 | 10 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&={\frac {1}{2}}\left(8+2{\sqrt {3}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 9.173a^{2}\\V&={\frac {1}{12}}{\sqrt {233+90{\sqrt {5}}+12{\sqrt {50+20{\sqrt {5}}}}}}a^{3}\\&\approx 1.9562a^{3}\end{aligned}} |
| 53 | Biaugmented pentagonal prism |  | 12 | 23 | 13 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&={\frac {1}{2}}a^{2}\left(6+4{\sqrt {3}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)\\&\approx 9.9051a^{2}\\V&={\frac {1}{12}}a^{3}{\sqrt {257+90{\sqrt {5}}+24{\sqrt {50+20{\sqrt {5}}}}}}\\&\approx 2.1919a^{3}\end{aligned}} |
| 54 | Augmented hexagonal prism |  | 13 | 22 | 11 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&=(5+4{\sqrt {3}})a^{2}\\&\approx 11.9282a^{2}\\V&={\frac {1}{6}}\left({\sqrt {2}}+9{\sqrt {3}}\right)a^{3}\\&\approx 2.8338a^{3}\end{aligned}} |
| 55 | Parabiaugmented hexagonal prism |  | 14 | 26 | 14 |  D_{2h} من الرتبة 8 |  {\begin{aligned}A&=(4+5{\sqrt {3}})a^{2}\\&\approx 12.6603a^{2}\\V&={\frac {1}{6}}\left(2{\sqrt {2}}+9{\sqrt {3}}\right)a^{3}\\&\approx 3.0695a^{3}\end{aligned}} |
| 56 | Metabiaugmented hexagonal prism |  | 14 | 26 | 14 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&=(4+5{\sqrt {3}})a^{2}\\&\approx 12.6603a^{2}\\V&={\frac {1}{6}}\left(2{\sqrt {2}}+9{\sqrt {3}}\right)a^{3}\\&\approx 3.0695a^{3}\end{aligned}} |
| 57 | Triaugmented hexagonal prism |  | 15 | 30 | 17 |  D_{3h} من الرتبة 12 |  {\begin{aligned}A&=3\left(1+2{\sqrt {3}}\right)a^{2}\\&\approx 13.3923a^{2}\\V&=\left({\frac {1}{\sqrt {2}}}+{\frac {3{\sqrt {3}}}{2}}\right)a^{3}\\&\approx 3.3052a^{3}\end{aligned}} |
| 58 | Augmented dodecahedron |  | 21 | 35 | 16 |  C_{5v} من الرتبة 10 |  {\begin{aligned}A&={\frac {1}{4}}\left(5{\sqrt {3}}+11{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 21.0903a^{2}\\V&={\frac {1}{24}}\left(95+43{\sqrt {5}}\right)a^{3}\\&\approx 7.9646a^{3}\end{aligned}} |
| 59 | Parabiaugmented dodecahedron |  | 22 | 40 | 20 |  D_{5d} من الرتبة 20 |  {\begin{aligned}A&={\frac {5}{2}}\left({\sqrt {3}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 21.5349a^{2}\\V&={\frac {1}{6}}\left(25+11{\sqrt {5}}\right)a^{3}\\&\approx 8.2661a^{3}\end{aligned}} |
| 60 | Metabiaugmented dodecahedron |  | 22 | 40 | 20 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&={\frac {5}{2}}\left({\sqrt {3}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 21.5349a^{2}\\V&={\frac {1}{6}}\left(25+11{\sqrt {5}}\right)a^{3}\\&\approx 8.2661a^{3}\end{aligned}} |
| 61 | Triaugmented dodecahedron |  | 23 | 45 | 24 |  C_{3v} من الرتبة 6 |  {\begin{aligned}A&={\frac {3}{4}}\left(5{\sqrt {3}}+3{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 21.9795a^{2}\\V&={\frac {5}{8}}\left(7+3{\sqrt {5}}\right)a^{3}\\&\approx 8.5676a^{3}\end{aligned}} |
| 62 | Metabidiminished icosahedron |  | 10 | 20 | 12 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&={\frac {1}{2}}\left(5{\sqrt {3}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 7.7711a^{2}\\V&={\frac {1}{6}}\left(5+2{\sqrt {5}}\right)a^{3}\\&\approx 1.5787a^{3}\end{aligned}} |
| 63 | Tridiminished icosahedron |  | 9 | 15 | 8 |  C_{3v} من الرتبة 6 |  {\begin{aligned}A&={\frac {1}{4}}\left(5{\sqrt {3}}+3{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 7.3265a^{2}\\V&=\left({\frac {5}{8}}+{\frac {7{\sqrt {5}}}{24}}\right)a^{3}\\&\approx 1.2772a^{3}\end{aligned}} |
| 64 | Augmented tridiminished icosahedron |  | 10 | 18 | 10 |  C_{3v} من الرتبة 6 |  {\begin{aligned}A&={\frac {1}{4}}\left(7{\sqrt {3}}+3{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 8.1925a^{2}\\V&={\frac {1}{24}}\left(15+2{\sqrt {2}}+7{\sqrt {5}}\right)a^{3}\\&\approx 1.395a^{3}\end{aligned}} |
| 65 | Augmented truncated tetrahedron |  | 15 | 27 | 14 |  C_{3v} من الرتبة 6 |  {\begin{aligned}A&={\frac {1}{2}}\left(6+13{\sqrt {3}}\right)a^{2}\\&\approx 14.2583a^{2}\\V&={\frac {11}{2{\sqrt {2}}}}a^{3}\\&\approx 3.8891a^{3}\end{aligned}} |
| 66 | Augmented truncated cube |  | 28 | 48 | 22 |  C_{4v} من الرتبة 8 |  {\begin{aligned}A&=(15+10{\sqrt {2}}+3{\sqrt {3}})a^{2}\\&\approx 34.3383a^{2}\\V&=\left(8+{\frac {16{\sqrt {2}}}{3}}\right)a^{3}\\&\approx 15.5425a^{3}\end{aligned}} |
| 67 | Biaugmented truncated cube |  | 32 | 60 | 30 |  D_{4h} من الرتبة 16 |  {\begin{aligned}A&=2\left(9+4{\sqrt {2}}+2{\sqrt {3}}\right)a^{2}\\&\approx 36.2419a^{2}\\V&=(9+6{\sqrt {2}})a^{3}\\&\approx 17.4853a^{3}\end{aligned}} |
| 68 | Augmented truncated dodecahedron |  | 65 | 105 | 42 |  C_{5v} من الرتبة 10 |  {\begin{aligned}A&={\frac {1}{4}}\left(20+25{\sqrt {3}}+110{\sqrt {5+2{\sqrt {5}}}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 102.1821a^{2}\\V&=\left({\frac {505}{12}}+{\frac {81{\sqrt {5}}}{4}}\right)a^{3}\\&\approx 87.3637a^{3}\end{aligned}} |
| 69 | Parabiaugmented truncated dodecahedron |  | 70 | 120 | 52 |  D_{5d} من الرتبة 20 |  {\begin{aligned}A&={\frac {1}{2}}\left(20+15{\sqrt {3}}+50{\sqrt {5+2{\sqrt {5}}}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 103.3734a^{2}\\V&={\frac {1}{12}}\left(515+251{\sqrt {5}}\right)a^{3}\\&\approx 89.6878a^{3}\end{aligned}} |
| 70 | Metabiaugmented truncated dodecahedron |  | 70 | 120 | 52 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&={\frac {1}{2}}\left(20+15{\sqrt {3}}+50{\sqrt {5+2{\sqrt {5}}}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 103.3734a^{2}\\V&={\frac {1}{12}}\left(515+251{\sqrt {5}}\right)a^{3}\\&\approx 89.6878a^{3}\end{aligned}} |
| 71 | Triaugmented truncated dodecahedron |  | 75 | 135 | 62 |  C_{3v} من الرتبة 6 |  {\begin{aligned}A&={\frac {1}{4}}\left(60+35{\sqrt {3}}+90{\sqrt {5+2{\sqrt {5}}}}+3{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 104.5648a^{2}\\V&={\frac {7}{12}}\left(75+37{\sqrt {5}}\right)a^{3}\\&\approx 92.0118a^{3}\end{aligned}} |
| 72 | Gyrate rhombicosidodecahedron |  | 60 | 120 | 62 |  C_{5v} من الرتبة 10 |  {\begin{aligned}A&=\left(30+5{\sqrt {3}}+3{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 59.306a^{2}\\V&=\left(20+{\frac {29{\sqrt {5}}}{3}}\right)a^{3}\\&\approx 41.6153a^{3}\end{aligned}} |
| 73 | Parabigyrate rhombicosidodecahedron |  | 60 | 120 | 62 |  D_{5d} من الرتبة 20 |  {\begin{aligned}A&=\left(30+5{\sqrt {3}}+3{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 59.306a^{2}\\V&=\left(20+{\frac {29{\sqrt {5}}}{3}}\right)a^{3}\\&\approx 41.6153a^{3}\end{aligned}} |
| 74 | Metabigyrate rhombicosidodecahedron |  | 60 | 120 | 62 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&=\left(30+5{\sqrt {3}}+3{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 59.306a^{2}\\V&=\left(20+{\frac {29{\sqrt {5}}}{3}}\right)a^{3}\\&\approx 41.6153a^{3}\end{aligned}} |
| 75 | Trigyrate rhombicosidodecahedron |  | 60 | 120 | 62 |  C_{3v} من الرتبة 6 |  {\begin{aligned}A&=\left(30+5{\sqrt {3}}+3{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 59.306a^{2}\\V&=\left(20+{\frac {29{\sqrt {5}}}{3}}\right)a^{3}\\&\approx 41.6153a^{3}\end{aligned}} |
| 76 | Diminished rhombicosidodecahedron |  | 55 | 105 | 52 |  C_{5v} من الرتبة 10 |  {\begin{aligned}A&={\frac {1}{4}}\left(100+15{\sqrt {3}}+10{\sqrt {5+2{\sqrt {5}}}}+11{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 58.1147a^{2}\\V&=\left({\frac {115}{6}}+9{\sqrt {5}}\right)a^{3}\\&\approx 39.2913a^{3}\end{aligned}} |
| 77 | Paragyrate diminished rhombicosidodecahedron |  | 55 | 105 | 52 |  C_{5v} من الرتبة 10 |  {\begin{aligned}A&={\frac {1}{4}}\left(100+15{\sqrt {3}}+10{\sqrt {5+2{\sqrt {5}}}}+11{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 58.1147a^{2}\\V&=\left({\frac {115}{6}}+9{\sqrt {5}}\right)a^{3}\\&\approx 39.2913a^{3}\end{aligned}} |
| 78 | Metagyrate diminished rhombicosidodecahedron |  | 55 | 105 | 52 |  C_{s} من الرتبة 2 |  {\begin{aligned}A&={\frac {1}{4}}\left(100+15{\sqrt {3}}+10{\sqrt {5+2{\sqrt {5}}}}+11{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 58.1147a^{2}\\V&=\left({\frac {115}{6}}+9{\sqrt {5}}\right)a^{3}\\&\approx 39.2913a^{3}\end{aligned}} |
| 79 | Bigyrate diminished rhombicosidodecahedron |  | 55 | 105 | 52 |  C_{s} من الرتبة 2 |  {\begin{aligned}A&={\frac {1}{4}}\left(100+15{\sqrt {3}}+10{\sqrt {5+2{\sqrt {5}}}}+11{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 58.1147a^{2}\\V&=\left({\frac {115}{6}}+9{\sqrt {5}}\right)a^{3}\\&\approx 39.2913a^{3}\end{aligned}} |
| 80 | Parabidiminished rhombicosidodecahedron |  | 50 | 90 | 42 |  D_{5d} من الرتبة 20 |  {\begin{aligned}A&={\frac {5}{2}}\left(8+{\sqrt {3}}+2{\sqrt {5+2{\sqrt {5}}}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 56.9233a^{2}\\V&={\frac {5}{3}}\left(11+5{\sqrt {5}}\right)a^{3}\\&\approx 36.9672a^{3}\end{aligned}} |
| 81 | Metabidiminished rhombicosidodecahedron |  | 50 | 90 | 42 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&={\frac {5}{2}}\left(8+{\sqrt {3}}+2{\sqrt {5+2{\sqrt {5}}}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 56.9233a^{2}\\V&={\frac {5}{3}}\left(11+5{\sqrt {5}}\right)a^{3}\\&\approx 36.9672a^{3}\end{aligned}} |
| 82 | Gyrate bidiminished rhombicosidodecahedron |  | 50 | 90 | 42 |  C_{s} من الرتبة 2 |  {\begin{aligned}A&={\frac {5}{2}}\left(8+{\sqrt {3}}+2{\sqrt {5+2{\sqrt {5}}}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 56.9233a^{2}\\V&={\frac {5}{3}}\left(11+5{\sqrt {5}}\right)a^{3}\\&\approx 36.9672a^{3}\end{aligned}} |
| 83 | Tridiminished rhombicosidodecahedron |  | 45 | 75 | 32 |  C_{3v} من الرتبة 6 |  {\begin{aligned}A&={\frac {1}{4}}\left(60+5{\sqrt {3}}+30{\sqrt {5+2{\sqrt {5}}}}+9{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 55.732a^{2}\\V&=\left({\frac {35}{2}}+{\frac {23{\sqrt {5}}}{3}}\right)a^{3}\\&\approx 34.6432a^{3}\end{aligned}} |
| 84 | Snub disphenoid |  | 8 | 18 | 12 |  D_{2d} من الرتبة 8 |  {\begin{aligned}A&=3{\sqrt {3}}a^{2}\\&\approx 5.1962a^{2}\\V&\approx 0.8595a^{3}\end{aligned}} |
| 85 | Snub square antiprism |  | 16 | 40 | 26 |  D_{4d} من الرتبة 16 |  {\begin{aligned}A&=2\left(1+3{\sqrt {3}}\right)a^{2}\\&\approx 12.3923a^{2}\\V&\approx 3.6012a^{3}\end{aligned}} |
| 86 | Sphenocorona |  | 10 | 22 | 14 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&=(2+3{\sqrt {3}})a^{2}\\&\approx 7.1962a^{2}\\V&={\frac {1}{2}}a^{3}{\sqrt {1+3{\sqrt {\frac {3}{2}}}+{\sqrt {13+3{\sqrt {6}}}}}}\\&\approx 1.5154a^{3}\end{aligned}} |
| 87 | Augmented sphenocorona |  | 11 | 26 | 17 |  C_{s} من الرتبة 2 |  {\begin{aligned}A&=(1+4{\sqrt {3}})a^{2}\\&\approx 7.9282a^{2}\\V&={\frac {1}{2}}a^{3}{\sqrt {1+3{\sqrt {\frac {3}{2}}}+{\sqrt {13+3{\sqrt {6}}}}}}+{\frac {1}{3{\sqrt {2}}}}\\&\approx 1.7511a^{3}\end{aligned}} |
| 88 | Sphenomegacorona |  | 12 | 28 | 18 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&=2\left(1+2{\sqrt {3}}\right)a^{2}\\&\approx 8.9282a^{2}\\V&\approx 1.9481a^{3}\end{aligned}} |
| 89 | Hebesphenomegacorona |  | 14 | 33 | 21 |  C_{2v} من الرتبة 4 |  {\begin{aligned}A&={\frac {3}{2}}\left(2+3{\sqrt {3}}\right)a^{2}\\&\approx 10.7942a^{2}\\V&\approx 2.9129a^{3}\end{aligned}} |
| 90 | Disphenocingulum |  | 16 | 38 | 24 |  D_{2d} من الرتبة 8 |  {\begin{aligned}A&=(4+5{\sqrt {3}})a^{2}\\&\approx 12.6603a^{2}\\V&\approx 3.7776a^{3}\end{aligned}} |
| 91 | Bilunabirotunda |  | 14 | 26 | 14 |  D_{2h} من الرتبة 8 |  {\begin{aligned}A&=\left(2+2{\sqrt {3}}+{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 12.346a^{2}\\V&={\frac {1}{12}}\left(17+9{\sqrt {5}}\right)a^{3}\\&\approx 3.0937a^{3}\end{aligned}} |
| 92 | Triangular hebesphenorotunda |  | 18 | 36 | 20 |  C_{3v} من الرتبة 6 |  {\begin{aligned}A&={\frac {1}{4}}\left(12+19{\sqrt {3}}+3{\sqrt {5\left(5+2{\sqrt {5}}\right)}}\right)a^{2}\\&\approx 16.3887a^{2}\\V&=\left({\frac {5}{2}}+{\frac {7{\sqrt {5}}}{6}}\right)a^{3}\\&\approx 5.1087a^{3}\end{aligned}} |