Impossible? No, just unlikely. The Amore Ambigram shown here is a nice short symmetric ambigram that is a good example of the letters in one orientation flipping over to become different letters in another orientation.

See this example of how this typographical marvel says 'Amore' one way and also says 'Amore' the other way. For a mental work-out, try to read it upside-down without rotating it (you can mouse over it at any time to make it spin).

If you wish, you can create other ambigrams by clicking the Create New Design button here.

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