| Name | Groups | #Vertices | Vertex orders | #Faces | Face orders | #Edges | Conway |
|---|---|---|---|---|---|---|---|
| Great Dodecahedron | dmccooeyKepler-Poinsotconcave | 12 | 12{5} | 12 | 12{5} | 22 | k(h=-0.2)I |
| Great Icosahedron | dmccooeyKepler-Poinsotconcave | 12 | 12{5} | 20 | 20{3} | 30 | k(h=-0.2)k(h=1)D |
| Great Stellated Dodecahedron Stellated Great Dodecahedron | dmccooeyKepler-Poinsotconcave | 20 | 20{3} | 12 | 12{5} | 30 | k(h=1.6)I |
| Small Stellated Dodecahedron Stellated Dodecahedron | dmccooeyKepler-Poinsotconcave | 12 | 12{5} | 12 | 12{5} | 22 | k(h=1)D |