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Plenty of kanji are symmetrical on the y-axis and x-axis. Plenty of kanji are symmetrical only on the y-axis.

What are some kanji that are only symmetrical on the x-axis? I don't know one.

What kanji change into another kanji when they are rotated and/or flipped? Here is one that I know:
干 -- flip --> 士

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    「曰」. Which is not the same as 「日」. Also, 「人」 is not symmetrical, only its gothic form is (its mirror is 「入」). – Ignacio Vazquez-Abrams Oct 19 '13 at 1:57
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    Sometimes symmetry depends on how you write them. I've seen people write 女 in a way that's left-right symmetrical, for example. – snailcar Oct 19 '13 at 3:53
  • @snailboat: You mean when it looks like without the lower horizontal stroke, and strokes barely cross at the bottom right corner? – istrasci Oct 19 '13 at 22:00
  • @kinyo: FYI, flipping vertically is not the same rotating 180°. Those two actions will only produce the same result if the character is symmetric about the vertical axis. Rotating the letter N by 180° will give the same letter, but flipping it vertically will give и . – istrasci Oct 19 '13 at 22:18
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    @istrasci Ah, I saw the near-symmetrical 女 again and I took a picture! i.stack.imgur.com/CyTar.png – snailcar Oct 29 '13 at 21:32
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Here's two that have just horizontal symmetry, at least in some fonts: 旧 咺

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巨 臣 排 区 州 唱, etc. but this is for fun only. Some are not as symetrical as others.

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