This is a Truncated Sphere D16. It has a 4-fold symmetry.
This die is inspired by the repulsion force polyhedra. In fact, the underlying polyhedron (not rounded) looks like one of the two shapes that can be obtained through this technique with 16 points repulsing each others. But in this case, I calculated the positions of those points to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere. The result is a truncated sphere with 16 circular faces of same radius.