What is a symmetry of order 4 for an equalateral triangular prism?
I am sorry but there is no symmetry of order 4. Having listed all 12 symmetries, I have found their orders as 1x 1 (identity) 7x 2 (4 reflections and 3 rotations from the centre of rect. face to the centre of opposite edge) 2x 3 (“xy” rotations through the centres of the triangular faces) 2x 6 (mixed operation: z reflection + xy rotation) Mathematically speaking, the symmetry group of this object is isomorphic to S3 x Z2. The former has elements of orders 1, 2, and 3, and the latter of 1 and 2. In a direct product, the order of an element g*h is the least common multiplier of the orders of g and h. There is no way of getting a least common multipler of 4 from {1,2,3} and {1,2}.
