# Thread: symmetries of composite objects

1. ## symmetries of composite objects

what are the symmetries of a triangulate prism (5 faces).top and base are equilateral triangles and 3 identical rectangular faces.
I cant help making it look harder than it really is ( i suspect).

2. Well, you can rotate about the line through the centers of both the top and bottom triangles through an angle of $\displaystyle 2\pi/3$ radians multiple times. 3 times gets you back to your starting point. You can also flip the prism (interchange top and bottom) followed by a rotation through $\displaystyle \pi/3$ radians about the axis through the centers of the top and bottom. Finally, you can rotate about an axis going through one lengthwise edge, the center of the prism, and the center of the opposite face. That rotation would be through $\displaystyle \pi$ radians.

Those are all the symmetries I can think of.

3. Thanks Ackbeet,
Now how would you write down all the symmetries as permutations of the set (1,2,3,4,5).
I now know that this prism has 12 symmetries (after applying a certain strategy),but am now unable to describe these geometrically without thinking I 'm doing it all wrong.
Pls help.Hommework to be submitted in <3days.
My excuse is toddlers and a new baby amongst everything else.

4. Hmm. I am neither able nor willing to help you any more. If this problem is for a homework, then it counts towards a grade. Forum policy is not knowingly to help with a problem that counts towards a grade.

In addition, I have no idea how to write down these symmetries as permutations of the set (1,2,3,4,5).