A Wolf Tooth cube is a strange and interesting puzzle. It is almost like solving two puzzles at once. In essence it is a cube and an octahedron intersected. Each of the six cube faces has one of the octahedron vertices in the centre, a square based pyramid with four different colours on it. Each of the eight octahedron faces has one of the cube vertices in the centre, a triangular based pyramid with three different colours on it.

The arrangement of colours on the cube part are as follows:

Red is opposite Orange

White is opposite Yellow

Blue is opposite Green

Red White and Blue appear clockwise on their shared vertex

The arrangement of colours on the octahedron part are as follows:

Red is opposite White

Yellow is opposite Silver

Purple is opposite Blue

Orange is opposite Green

Red Yellow Purple and Orange appear clockwise around their shared vertex

It is possible to orient the octahedron through the cube such that none of the same colours on the cube and octahedron are in contact?

If so what four colours appear on the octahedron vertex in the middle of the green cube face?

To illustrate the objective of the puzzle, in the cube above the white cube face and the white octahedron face are not in contact, whereas the green cube face and the green octahedron face are in contact, which is not permitted within this puzzle.

(For the purposes of this puzzle I have changed the order of the colours on the octahedron part from the colouring on an actual Wolf Tooth cube, shown here.)