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So here's the situation:
oX and oY are what I have transform-origin set to, with a Z coordinate of 0. I want to be able to rotate around the axis drawn, with an arbitrary origin. How? I don't understand how CSS3's rotate3D(x,y,z,rotate) works.

Awfully drawn diagram of 3D plane

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Here you have good examples of how to flip: css3playground.com/flip-card.php –  Vucko Nov 1 '12 at 12:12

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up vote 1 down vote accepted

To solve this, I had to apply the perspective() modifier on the parent container - so that the rotate3D() is in the correct context.

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