Yes, the Yin-Yang sign has symmetry.
Another take:
No, the Yin and Yang are not symmetric. In order for symmetry any mirror image of the Yin-Yang must be indistinguishable from the original. In order to test and visualize this, take a Yin-Yang image into an editing tool like Photoshop. Convert the Yin-Yang to a negative (swap white for black and vice versa, which is the same as rotating it 180 degrees), and then perform a horizontal flip. This is the same as viewing the image in a mirror.
Compare to the original. Does it look the same?
The yinyang symbol has exactly as much white as black, so the ratio is 1:1.
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a yin-yang symbol has point symmetry but no line symmetry so 0
A division sign (÷) has two lines of symmetry. One line of symmetry runs vertically through the center, and the other runs horizontally through the center. This means the division sign is symmetrical along both the vertical and horizontal axes.
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David Kunstatter goes by YinYang.
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Hokkaido, Honshu, Shikoku, and Kyushu