help - radial mirror inner faces

[claus82]

Hello,+ I would like to create chess, so i made "slices" in order to mirror them, but when I use the mirror the pieces have inner faces, look pics.
If I try to dissolve the faces/edges/vertices then the geometries mess up... Any help appreciated!
Cheers

https://drive.google.com/open?id=1stD17-...pDAPySsIF6

https://drive.google.com/open?id=1htFAJf...RaZclgCdL2