Approximate Symmetry is approximately symmetrical. Regular Symmetry is Symmetrical for sure.
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Lines of symmetry are 2 dimensional. Planes of symmetry are 3D.
Line or reflective symmetry is really a special case of rotational symmetry but from a different viewpoint. In line symmetry imagine a line going north to south on the page. If you rotate an image out of the page around that line through 180 degrees you get a reflection. For rotational symmetry imagine that same line being perpendicular to the page so that you see it as a dot. The image is then rotated around that dot.
Symmetry is important in an organizational sense. It makes a difference in biology, mineralogy and physics. Its importance also touches on physical laws.
A regular octagon has 8 lines of symmetry. See the Related Link below that includes a diagram of an octagon with the lines of symmetry drawn. A non-symmetrical octagon may have between 0-4 lines of symmetry.
8.