Here's something:  
>! [![enter image description here][1]][1]  
>! RGB and CMY form two "triangles", so each of the groups of three is touching its other members - the only tricky part is making every side of one triangle touch the other triangle.  
>! Cyan is tangent to Green at the spot it's supposed to touch, Magenta and Yellow are tangent to Blue.

Alternatively, if you actually need connectedness,  
>! connecting them in a cycle still works:  
>! [![enter image description here][2]][2]  
>! Here, white squares are "dots" and grey squares are interior intersections.


  [1]: https://i.sstatic.net/8cQka.png
  [2]: https://i.sstatic.net/nlepI.png