It is geodesic polyhedron {3,5+}3,0, with pentavalent vertices separated by an edge-direct distance of 3 steps.
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.
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.