If I create a rigid polygon with the appropriate icon, clicking on the points that define it, then I can move it like all the objects (with the mouse) and is actually it behaves like a rigid polygon.
The same happens if I define the rigid polygon with the command RigidPolygon[A,B,C,...] with pre.existing points A, B, C,...
:( BUT if I create a rigid polygon with the command RigidPolygon includind numerically defined points, for instance RigidPolygon[ (1,1), (3,1), (2,5), (2,3)] and I try to move it like all the objects (with the mouse) the polygon is not rigid, it changes (randomly?) their shape. :(
I think that it should be possible to move it without changing the shape! It has been defined like a "rigid" polygon!
[size=85](Please note that when defining thus the rigid polygon appears only the second vertex, not the first and the second like occurs with rigid polygons defined otherwise)[/size]
The same problem 
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