Here's a design to flip over.
The fairly long Worldpeace Deaddream ambigram displayed to the left is a good example of the letters in one orientation flipping over to become different letters in another orientation.
A quick glance will show you that you can read this as 'Worldpeace' when the design is upright and as 'Deaddream' when the design is inverted.
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).
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