what is mean by four fold symmetry?

Question

anonymous · Answer

Axis of Symmetry is a line that divides the figure into two symmetrical parts in such a way that the figure on one side is the mirror image of the figure on the other side.

chmvijay · Answer

if u rotate the figure by 90, 180 ,270,360 degrees through its principal axis u get the same image as that of not rotated

chmvijay · Answer

hence it is called 4 fold rotation symmetry

anonymous · Answer

A good visual chemistry-related example is one from somebody else I was helping: http://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/D_orbitals.svg/2000px-D_orbitals.svg.png (look at all all of them except: the combined D-orbital, and d$\large_{z^2}$; those 4 of them have this type of symmetry, agreed?) How to check? Take one of those lobes and turn it 90$^o$ along the plane. Then another 90$^o$. Then another 90$^o$. Then another 90$^o$. Hmm, what do you know they are all the same :D Another way to think of this visually is this: fold a paper in half, then half again. Unfold and how many flat parts do you have separated by the creases? Like if you cut along the creases how many smaller pieces of paper do you have? 4 right? Same principle.