Moreover, the colour,
which is assigned to the central vertex or to the outer face, can be used at most k+1 times. If the central vertex and the outer
face are coloured with the same colour, none other element can be coloured with this colour. In this case the remaining four
colours can be used each at most 2k times and then there remain at least four uncoloured elements. If the central vertex and
the outer face are coloured with different colours, then these two colours are used together on at most 2k+2 elements.