Hi Moffat, I’ve ‘proved’ it can’t be done in fewer than four colours. I converted each dice net into an ‘island’ and had lines representing bridges between islands. There was, unfortunately, an island surrounded by, and connected to, an odd number (5) of other islands, all of which were connected in a circle around the central island. The result was like a spider’s web with 5 spokes. Clearly the central island would have to be a different colour from the surrounding islands. The surrounding islands would have to alternate two colours around the outside circle in order to attempt to limit the total required colours to three. Alas because five is an odd number, we would get (e.g.) red, green, red, green, red, which if connected in circular fashion would result in two reds next to each other (I’m assuming the central island is (e.g.) blue). Hence the need for a fourth colour such that the outside ring is red, green, red, green, yellow. Then yellow is adjacent to the first red. Sorry it’s a bit long winded. Hope it makes sense!