Consider the following problem: given two copies of a regular tetrahedron, glue these two copies together along a face. Describe the rotational symmetries of the resulting solid.
My approach. The rotations are:
- the identity
- two rotations about the axis connecting two vertices and the center of the common face
- one rotation for each of the three axis passing through the three vertices of the common face and the opposite edge of the common face
for a total of 6 rotations. Am I right?