Planets Puzzle

This is a Very difficult Puzzle

Description

Invented by renowned puzzle master Oskar van Deventer, the Planets Puzzle is rather hard to solve for two reasons:

First of all, it is not entirely clear what constitutes a position, and secondly, the arrangement of irregular craters blocks many orientations of the planets.

There are only six craters on each of the planets but if we were to add some, extending the arrangement of the existing ones, then a planet would have 12 craters.
They are arranged like the vertices of a cuboctahedron. I will only count a planet's orientations where at least two of these 12 points are in contact with the three others planets.

A planet cannot have craters at all three contact points.

There are eight ways a planet can have craters at two specified contact points (24 ways for craters at any two contacts).

There are 20 ways a planet can have a crater at exactly one specified contact point (60 ways for a single crater at any one contact).

There are twelve ways a planet can have no craters at the three contact points.

Good luck!