iregular polygon symmetry

[ainne power]

HI after plotting the points (3,3) (-2,2) (-3-3) and (2-2) and joining the points on the graph I have constructed a quadrilateral shape, I am trying to figure the elements of the symmetry group of this shape, so far I have the identity element and a rotation about pi , I cant seem to find any reflections can this shape be reflected in the x or y axis, or does this have reflections as it is an irregular polygon
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[lookagain]

Those points give you a parallelogram, all sides equal;
where does "irregular polygon" come from

It's irregular because it does not have all of its sides equal together with all of
its internal angles equal. <------- edit

And, just because it's a parallelogram, that doesn't mean all sides are equal.
This is a special case of one that is also a rhombus.

I cant seem to find any reflections can this shape be reflected in the x or y axis, ...
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Reflecting it across the x-axis alone does not give the same shape.

Reflecting it across the y-axis alone does not give the same shape.

Reflecting it across both the x-axis and the y-axis does give the same shape,
because it has origin symmetry.


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[lookagain]

Are you saying that the sides here:
"after plotting the points (3,3) (-2,2) (-3,-3) and (2,-2)"
are not equal? You must have had too much Easter wine :cool:

There was wrong wording. Both conditions were not satisfied together.

It's irregular because it does not have all of its sides equal, together with all of
its internal angles equal. <------- edit

It certainly does have all of its sides equal in length.

 

[Deleted member 4993]

Those points give you a parallelogram, all sides equal;
where does "irregular polygon" come from

This polygon is irregular because:

A regular polygon is an

-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular and equilateral). Only certain regular polygons are "constructible" using the classical Greek tools of the compass and straightedge. (Wolfram).

Among quadrilaterals, only square is a regular polygon.

Now fate worse than "watching cricket" → go join LA in the corner and exchange niceties ....