Here's something:

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.

Here's something:

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:

Here, white squares are "dots" and grey squares are interior intersections.