What does having 3d symmetry 2d symmetry and 1d symmetry mean?

In summary, 3D symmetry refers to an object's invariance under three-dimensional transformations, such as rotation and reflection, allowing it to look the same from multiple angles. 2D symmetry involves similar invariance but within a two-dimensional plane, where shapes can be symmetrical through reflections or rotations in that plane. 1D symmetry pertains to one-dimensional objects or lines, which can exhibit symmetry through reflections across a central point or line segment. Each type of symmetry highlights different ways that objects can be balanced and harmonious in their structure.
  • #36
haruspex said:
@Orodruin has explained to me that the point being considered is on the x axis. Consequently ##\vec E_y=\vec E_z=0## is consistent with the field being normal to the cylinder's axis. What made you think it was not?
haruspex said:
The field is everywhere normal to the cylinder axis
The y axis is also normal to the cylinder's axis...
But I think I get it it also depends on where the reference point is...so
 
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  • #37
tellmesomething said:
The y axis is also normal to the cylinder's axis...
But I think I get it it also depends on where the reference point is...so
Yes, ##\vec E(x\hat x)=f(x)\hat x##, so no ##\hat y## or ##\hat z## term.
 
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