| Name | Groups | #Vertices | Vertex orders | #Faces | Face orders | #Edges | Conway |
|---|---|---|---|---|---|---|---|
| Ditrigonal Dodecadodecahedron | dmccooeySelf-Intersecting Quasi-Regularconcave | 20 | 20{6} | 24 | 24{5} | 42 | |
| Dodecadodecahedron | dmccooeySelf-Intersecting Quasi-Regularconcave | 30 | 30{4} | 24 | 24{5} | 52 | |
| Great Ditrigonal Icosidodecahedron | dmccooeySelf-Intersecting Quasi-Regularconcave | 20 | 20{6} | 32 | 12{5}+20{3} | 50 | |
| Great Icosidodecahedron | dmccooeySelf-Intersecting Quasi-Regularconcave | 30 | 30{4} | 32 | 12{5}+20{3} | 60 | |
| Small Ditrigonal Icosidodecahedron | dmccooeySelf-Intersecting Quasi-Regularconcave | 20 | 20{6} | 32 | 12{5}+20{3} | 50 |