2 a Describe carefully the action of the rotation group of the regular tetrahedron on its set of faces describing the face orbits for each rotation 4 marks b Use your answer to compute the number of non equivalent ways to colour the faces of a regular tetrahedron using 5 colours where two colourings are equivalent if one can be rotated onto the other Show your working 8 marks c Give a general formula for the number of different coloured tetradheda that can be manufactured using k colours and use your formula to find the minimum number of colours required to produce at least 1 000 different colourings 3 marks