| Symmetry group | name | edges | dual | Vertex configuration | vertices | face | Properties |
|---|---|---|---|---|---|---|---|
| c1 | Augmented truncated cube | 48 | 2.4+8(3.82)$#$8(3.43)$#$16(3.4.3.8) | 28 | Equilateral triangle, Triangle | ||
| cs | Augmented truncated dodecahedron | 105 | 4.5+3.10(3.102)$#$5(3.4.5.4)$#$10(3.4.3.10) | 65 | Equilateral triangle, Triangle | ||
| ci | Augmented truncated tetrahedron | 27 | 2x3(3.62)$#$3(3.4.3.4)$#$6(3.4.3.6) | 15 | Equilateral triangle, Triangle | ||
| c2 | Biaugmented pentagonal prism | 23 | 2(42.5)$#$2(34)$#$2x4(32.4.5) | 12 | Equilateral triangle | ||
| c3 | Biaugmented triangular prism | 17 | 2(35)$#$2(34)$#$4(33.4) | 8 | Equilateral triangle, Triangle |