This is a Truncated Sphere D13. It has a 4-fold symmetry.
This die is inspired by the
repulsion force polyhedra. But in this case, the underlying polyhedron (not rounded) does not exactly look like the shape that can be obtained through this technique with 13 points repulsing each others.
Instead, 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 13 circular faces of same radius.