This is an alternative Truncated Sphere D22. It has the same symmetries as the tetrahedron.
See the D22 with 5-fold symmetry for numbers located on the faces.
This die is inspired by the repulsion force polyhedra. In fact, the underlying polyhedron (not rounded) looks like the shape that can be obtained through this technique with 22 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 22 circular faces of same radius.