Suppose i have an equilateral triangle and i want to find the principal axes of rotation passing through one of the vertex. How can i do that? I am thinking along the following lines but i'm not too sure: 1)Since the equilateral triangle has symmetry about a median, that definitely is one principal axis. 2)Now, i want 2 axes such that those 2 axes and the centroidal axis which i found above are mutually perpendicular. The problem now, however, is that i don't have any "symmetry" to rely on. Sure i COULD think along this line now : "if i rotate the triangle 360 degrees about one of the sides, i would return to the original configuration, so let me choose that as one of the axis, which leaves me with only one choice for the third axis and voila!" But i am not too sure of my approach in 2nd point since it just doesn't seem right; rotating an object 360 degrees to get the original configuration isn't really a symmetry! 1) So, is there some fool-proof way i can use (and be 100% certain of being correct) to determine principal axes of rotation? 2) Maybe mathematical? 3) Also, how reliable is this symmetry approach i follow?