So all of Blender's mirror functions are axis mirroring.
I only know point mirroring / point reflexion from math in 2D. In 2D it's equal to a rotation of 180° around a chosen point.
Is there any way to do it in blender in 3D? Is point reflexion even possible in 3D?
EDIT: After putting more thought into this, it seems I'd need to mirror each point on the closest point on a surface similar to the object itself.
EDIT2: I played around with some python and vector math, but the results where horrible, so to say. It seems that this is not (easily) possible, except when splitting the mesh into several objects.
Top: standard mirroring