Thread: symmetry of hexagon in the plane?

a hexagon with vertices (1,0) (0,1) (-1,1)(-1,0) (0,-1) and (1,-1) how many rotational and reflection symmetry will it have , I need to sketch it and then using standard notion write down the elements of the symmetry group S(H) of H giving a brief description of the geometric effect of the each symmetry on point in the plane.!!!!

i know that its regular hexagon with all sides equal
and hence the symmetry would be {e,rpi/3, r 2pi/3 rpi, r 4pi/3, r5pi/3} but the description of geometric effect of the each of the point in the plane Is what I don't understand
can someone please check my understanding is clear
does this shape have reflection symmetry or not?

Originally Posted by livingdream

a hexagon with vertices (1,0) (0,1) (-1,1)(-1,0) (0,-1) and (1,-1) how many rotational and reflection symmetry will it have , I need to sketch it and then using standard notion write down the elements of the symmetry group S(H) of H giving a brief description of the geometric effect of the each symmetry on point in the plane.!!!!

i know that its regular hexagon with all sides equal
and hence the symmetry would be {e,rpi/3, r 2pi/3 rpi, r 4pi/3, r5pi/3} but the description of geometric effect of the each of the point in the plane Is what I don't understand
can someone please check my understanding is clear
does this shape have reflection symmetry or not?

Did you actually sketch it? If so, try drawing a more accurate sketch and you will see that it is not a "regular hexagon with all sides equal". A careful sketch will also enable you to see which rotations and reflections are symmetries of this hexagon.

sorry if I said its a regular hexagon- what I meant was I know regualr hexagon has 6 symmetry of rotation anf reflection. I actually drawn this accuratley and can only find reflection on y=x and y=-x line that is 45, 135, 225 and 315 degrees and in terms of rotation it only rotates back on it self once through 360 degree

Originally Posted by Opalg

Did you actually sketch it? If so, try drawing a more accurate sketch and you will see that it is not a "regular hexagon with all sides equal". A careful sketch will also enable you to see which rotations and reflections are symmetries of this hexagon.

Originally Posted by livingdream

sorry if I said its a regular hexagon- what I meant was I know regualr hexagon has 6 symmetry of rotation anf reflection. I actually drawn this accuratley and can only find reflection on y=x and y=-x line that is 45, 135, 225 and 315 degrees and in terms of rotation it only rotates back on it self once through 360 degree

That is close to being correct, except that you have missed out on the rotation through 180º. You are correct that the only reflections are in the lines y=x and y=-x.

Originally Posted by Opalg

That is close to being correct, except that you have missed out on the rotation through 180º. You are correct that the only reflections are in the lines y=x and y=-x.

so my rotations will be r_(π ),e,and reflection i.e.q is q_(π/4) ,3π/4,5π/4,7π/4
is this correct