This list is far from complete, and may include duplicates.
| Name (link) | degree | vertices |
|---|
| K5 | 4 | 5 |
| K2,2,2 | 4 | 6 |
| K4,4 | 4 | 8 |
| K3 × K3 | 4 | 9 |
| K5 × K2 | 4 | 10 |
| cuboctahedron | 4 | 12 |
| C4 × K3 | 4 | 12 |
| 13-circulant(1,5) | 4 | 13 |
| hemi-icosidodecahedron | 4 | 15 |
| 15-circulant(1,4) | 4 | 15 |
| rectification of C5:{5,5} | 4 | 15 |
| C4 □ C4 | 4 | 16 |
| torus-s-4-1 | 4 | 17 |
| 6-cycle × 3-cycle | 4 | 18 |
| 20-circulant(1,9) | 4 | 20 |
| 21-circulant(1,8) | 4 | 21 |
| rectification of {3,6}(1,3) | 4 | 21 |
| torus-s-5-5 | 4 | 25 |
| rectification of {4,4}(3,2) | 4 | 26 |
| rectification of C11:{6,6} | 4 | 27 |
| rectification of {3,6}(3,3) | 4 | 27 |
| 28-circulant(1,13) | 4 | 28 |
| rectification of C7.2 | 4 | 28 |
| rectification of N10.6 | 4 | 30 |
| rectification of C5:{4,5} | 4 | 30 |
| rectification of C7:{4,6} | 4 | 30 |
| rectification of the icosahedron | 4 | 30 |
| rectification of S4:{5,5} | 4 | 30 |
| rectification of {4,4}(4,0) | 4 | 32 |
| rectification of {4,4}(4,1) | 4 | 34 |
| rectification of C10.3 | 4 | 36 |
| rectification of {4,4}(3,3) | 4 | 36 |
| rectification of {3,6}(0,4) | 4 | 36 |
| rectification of S4:{4,6} | 4 | 36 |
| rectification of {3,6}(2,4) | 4 | 39 |
| rectification of {4,4}(4,2) | 4 | 40 |
| rectification of C6:{4,5} | 4 | 40 |
| rectification of S5:{5,5} | 4 | 40 |
| rectification of N10.1 | 4 | 48 |
| rectification of N22.4 | 4 | 48 |
| rectification of {3,6}(4,4) | 4 | 48 |
| rectification of S3:{3,8} | 4 | 48 |
| rectification of S5:{4,6} | 4 | 48 |
| rectification of R9.17 | 4 | 48 |
| rectification of R9.18 | 4 | 48 |
| rectification of {4,4}(4,3) | 4 | 50 |
| rectification of {4,4}(5,0) | 4 | 50 |
| rectification of {4,4}(5,1) | 4 | 52 |
| rectification of C11:{4,6} | 4 | 54 |
| rectification of R10.13 | 4 | 54 |
| rectification of R10.14 | 4 | 54 |
| rectification of C12.1 | 4 | 55 |
| rectification of C12.2 | 4 | 55 |
| rectification of {3,6}(1,5) | 4 | 57 |
| rectification of {4,4}(5,2) | 4 | 58 |
| rectification of C12{4,6}5 | 4 | 60 |
| rectification of N12.2 | 4 | 60 |
| rectification of N22.3 | 4 | 60 |
| rectification of R11.5 | 4 | 60 |
| rectification of S4:{4,5} | 4 | 60 |
| rectification of S6:{4,6} | 4 | 60 |
| rectification of R9.16 | 4 | 60 |
| rectification of {3,6}(3,5) | 4 | 63 |
| rectification of {4,4}(4,4) | 4 | 64 |
| rectification of R9.5 | 4 | 64 |
| rectification of R9.6 | 4 | 64 |
| rectification of {4,4}(5,3) | 4 | 68 |
| rectification of C18.1 | 4 | 68 |
| rectification of C10.2 | 4 | 72 |
| rectification of C19.2 | 4 | 72 |
| rectification of {4,4}(6,0) | 4 | 72 |
| rectification of {4,4}(6,1) | 4 | 74 |
| rectification of N37.5 | 4 | 75 |
| rectification of {3,6}(5,5) | 4 | 75 |
| rectification of S6:{3,10} | 4 | 75 |
| rectification of C27.7 | 4 | 78 |
| rectification of {4,4}(6,2) | 4 | 80 |
| rectification of S5:{4,5} | 4 | 80 |
| rectification of R9.14 | 4 | 80 |
| rectification of N29.2 | 4 | 81 |
| rectification of {3,6}(0,6) | 4 | 81 |
| rectification of {4,4}(5,4) | 4 | 82 |
| rectification of {3,6}(2,6) | 4 | 84 |
| rectification of N16.2 | 4 | 84 |
| rectification of N23.2 | 4 | 84 |
| rectification of N23.3 | 4 | 84 |
| rectification of N30.5 | 4 | 84 |
| rectification of N34.5 | 4 | 84 |
| rectification of N37.3 | 4 | 84 |
| rectification of N41.2 | 4 | 84 |
| rectification of N41.3 | 4 | 84 |
| rectification of N44.5 | 4 | 84 |
| rectification of N9.1 | 4 | 84 |
| rectification of N9.2 | 4 | 84 |
| rectification of R10.9 | 4 | 84 |
| rectification of R19.23 | 4 | 84 |
| rectification of S3:{3,7} | 4 | 84 |
| rectification of {4,4}(6,3) | 4 | 90 |
| rectification of N14.1 | 4 | 90 |
| rectification of {3,6}(4,6) | 4 | 93 |
| rectification of C17.3 | 4 | 96 |
| rectification of R17.20 | 4 | 96 |
| rectification of R17.21 | 4 | 96 |
| rectification of R17.22 | 4 | 96 |
| rectification of R21.15 | 4 | 96 |
| rectification of R21.16 | 4 | 96 |
| rectification of R21.19 | 4 | 96 |
| rectification of S5:{3,8} | 4 | 96 |
| rectification of R9.3 | 4 | 96 |
| rectification of R9.4 | 4 | 96 |
| rectification of {4,4}(7,0) | 4 | 98 |
| rectification of {4,4}(7,1) | 4 | 100 |
| rectification of C26.1 | 4 | 100 |
| rectification of {4,4}(5,5) | 4 | 100 |
| rectification of R16.3 | 4 | 100 |