Here I've put red dots on corners where six triangles meet and green dots on corners where five triangles meet:
This has too many red dots together to be the pentakis icosidodecahedron suggested by some commenters -- in particular, the two red-red-red triangles sharing an edge slightly below the middle of the image are not to be found in that polyhedron.
What it does look like to me is a pentakis icosidodecahedron that one has cut up along the one of the "equators" and then twisted one half by $36^\circ$ before gluing them together again.
This figure still has 80 sides rather than the claimed 65, though. But on the other hand, I can count 35 sides visible in this picture, and so many triangles should not be visible from one point in a somewhat regularly constructed 65-sided polyhedron anyway.
A systematic name for it would be a pentakis pentagonal orthobirotunda.