For how many months of the year does the north pole receive no insolation

For about six months there is no insolation on the north pole due to its position on the Earth and the Earth's position itself. When the Earth is in the December solstice, the earth is rotating around on a relatively higher plane. This phenomenon leads to the insolation of the north pole from approximately three months before and three months after the December solstice because it is too high far to receive the sun's rays.