Rocket Lab has successfully launched a rocket from New Zealand and placed several objects in orbit, see here for example. One payload is New Zealand's first satellite the Humanity Star, a reflective geodesic that can be seen at night by reflected light. According to this it has 65 sides.
What is the name for this shape?
Open image in new window for full size (source):
On
The picture on the right, if you look closely at the base, seems to show that the lowest pentagon on the underlying icosidodecahedron (or pentagonal orthobirotunda as some have observed) has not been augmented with five triangles. They may have left those off to provide a mounting surface. In that case there would be 75 triangular sides, so still 10 unaccounted for.
Edit: "picture on the right" is from this link https://space.stackexchange.com/questions/24616/does-humanity-star-have-non-reflective-triangular-panels-if-so-what-are-their
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.