Hi Andras, also I see now that trying to join only the 6 big pieces together does not give a solid - doing that and then selecting naked edges led me to this small irregularity in 2 corners of the shape:








There seems to be a tiny micro edge in those areas with a length of only 0.003 units - that's almost certainly what is interfering with filleting.

It looks like you may be able to fix that by selecting the 6 main pieces and using the Merge command:
http://moi3d.com/2.0/docs/moi_command_reference10.htm#merge

That should merge the micro edge with its much longer neighbor so it's all one single long edge.

I've attached a tuned up 3DM file where I did that - this one should probably behave better for you now.

- Michael