| bgcolor=#e7dcc3 colspan=2 | Hexapentakis truncated icosahedron | |
|---|---|---|
| align=center colspan=2 | ||
| Conway notation | ktI | |
| Geodesic polyhedron | 3,0 | |
| Faces | 180 | |
| Edges | 270 | |
| Vertices | 92 | |
| Face configuration | (60) V5.6.6 (120) V6.6.6 | |
| Symmetry group | Icosahedral (Ih) | |
| Dual polyhedron | Truncated pentakis dodecahedron | |
| Properties | convex |
Geodesic polyhedra are constructed by subdividing faces of simpler polyhedra, and then projecting the new vertices onto the surface of a sphere. A geodesic polyhedron has straight edges and flat faces that approximate a sphere, but it can also be made as a spherical polyhedron (A tessellation on a sphere) with true geodesic curved edges on the surface of a sphere. and spherical triangle faces.
| Conway | u3I = (kt)I | (k5)k6tI | (k)tI | Spherical ktI | |
|---|---|---|---|---|---|
| Image | |||||
| Form | 3-frequency subdivided icosahedron | 1-frequency subdivided hexakis truncated icosahedron | 1-frequency subdivided truncated icosahedron | Spherical polyhedron |
| Polyhedron | Truncated Icosahedron |
|
| Hexapentakis truncated Icosahedron | |
|---|---|---|---|---|---|
| Image | |||||
| Conway | tI | k5tI | k6tI | k5k6tI |
| bgcolor=#e7dcc3 colspan=2 | Pentakis truncated icosahedron | |
|---|---|---|
| align=center colspan=2 | ||
| Conway notation | k5tI | |
| Faces | 132: 60 triangles 20 hexagons | |
| Edges | 90 | |
| Vertices | 72 | |
| Symmetry group | Icosahedral (Ih) | |
| Dual polyhedron | Pentatruncated pentakis dodecahedron | |
| Properties | convex |
It is geometrically similar to the icosahedron where the 20 triangular faces are subdivided with a central hexagon, and 3 corner triangles.
Its dual polyhedron can be called a pentatruncated pentakis dodecahedron, a dodecahedron, with its vertices augmented by pentagonal pyramids, and then truncated the apex of those pyramids, or adding a pentagonal prism to each face of the dodecahedron. It is the net of a dodecahedral prism.
| bgcolor=#e7dcc3 colspan=2 | Hexakis truncated icosahedron | |
|---|---|---|
| align=center colspan=2 | ||
| Conway notation | k6tI | |
| Faces | 132: 120 triangles 12 pentagons | |
| Edges | 210 | |
| Vertices | 80 | |
| Symmetry group | Icosahedral (Ih) | |
| Dual polyhedron | Hexatruncated pentakis dodecahedron | |
| Properties | convex |
It is visually similar to the chiral snub dodecahedron which has 80 triangles and 12 pentagons.
The dual polyhedron can be seen as a hexatruncated pentakis dodecahedron, a dodecahedron with its faces augmented by pentagonal pyramids (a pentakis dodecahedron), and then its 6-valance vertices truncated.
It has similar groups of irregular pentagons as the pentagonal hexecontahedron.