| d | v | name | intersection array |
|---|---|---|---|
| 1 | 4 | K4 | {3;1} |
| 2 | 6 | K3,3 | {3,2;1,3} |
| 2 | 10 | Petersen | {3,2;1,1} |
| 3 | 8 | 3-cube | {3,2,1;1,2,3} |
| 3 | 14 | Heawood | {3,2,2;1,1,3} |
| 4 | 18 | Pappus | {3,2,2,1;1,1,2,3} |
| 4 | 28 | Coxeter | {3,2,2,1;1,1,1,2} |
| 4 | 30 | Tutte's 8-cage | {3,2,2,2;1,1,1,3} |
| 5 | 20 | Dodecahedron | {3,2,1,1,1;1,1,1,2,3} |
| 5 | 20 | Desargues | {3,2,2,1,1;1,1,2,2,3} |
| 6 | 126 | Tutte's 12-cage | {3,2,2,2,2,2;1,1,1,1,1,3} |
| 7 | 102 | Biggs-Smith | {3,2,2,2,1,1,1;1,1,1,1,1,1,3} |
| 8 | 90 | Foster | {3,2,2,2,2,1,1,1;1,1,1,1,2,2,2,3} |
Each is uniquely determined by the intersection array. All are distance-transitive, except for Tutte's 12-cage.