An 18-colouring of 3-space omitting distance one

It is known that the number of colours χ(R3) necessary to colour each point of 3-space so that no two points lying distance 1 apart have the same colour lies between 5 and 21. The upper bound of 21 was established by constructing a colouring with the 1-excluded property. In this paper a 1-excluded, 18-colouring is constructed.