| Name | Groups | #Vertices | Vertex orders | #Faces | Face orders | #Edges | Conway |
|---|---|---|---|---|---|---|---|
| Cube Hexahedron | dmccooeyPlatonicisohedronSpace-fillingisotoxal | 8 | 8{3} | 6 | 6{4} | 12 | C, jY3 |
| Dodecahedron Goldberg(0,1) | dmccooeyGoldbergPlatonicisohedronisotoxal | 20 | 20{3} | 12 | 12{5} | 30 | D, gY3 |
| Icosahedron | dmccooeyPlatonicisohedrondeltahedronGeodesic Icosahedraisotoxal | 12 | 12{5} | 20 | 20{3} | 30 | I, sY3, k5aY5 |
| Octahedron Square Dipyramid | dmccooeyPlatonicisohedrondeltahedronisotoxal | 6 | 6{4} | 8 | 8{3} | 12 | O, aY3 |
| Tetrahedron | dmccooeyPlatonicisohedrondeltahedronisotoxal | 4 | 4{3} | 4 | 4{3} | 6 | T, Y3 |