Hexapentakis truncated icosahedron

Pentakis truncated icosahedron
Conway notation	k5tI
Faces	132: 60 triangles 20 hexagons
Edges	90
Vertices	72
Symmetry group	Icosahedral (Ih)
Dual polyhedron	Pentatruncated pentakis dodecahedron
Properties	convex

The pentakis truncated icosahedron is a convex polyhedron constructed as an augmented truncated icosahedron, adding pyramids to the 12 pentagonal faces, creating 60 new triangular faces.

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.

Hexakis truncated icosahedron
Conway notation	k6tI
Faces	132: 120 triangles 12 pentagons
Edges	210
Vertices	80
Symmetry group	Icosahedral (Ih)
Dual polyhedron	Hexatruncated pentakis dodecahedron
Properties	convex

The hexakis truncated icosahedron is a convex polyhedron constructed as an augmented truncated icosahedron, adding pyramids to the 20 hexagonal faces, creating 120 new triangular faces.

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.