If everything else fails and you have to code it yourself then here are two pointers to algorithms (I hope you don’t need to go this way):
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GJK (Gilbert-Johnson-Keerthi) is a popular algorithm for collision detection of convex objects. Popular means there are lots of implementations on the web (with varying robustness).
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If it is pure triangle-triangle collision you are looking then perhaps this paper will help:
http://knight.cis.temple.edu/~lakaemper/courses/cis350_2004/etc/moeller_triangle.pdf
Both will be very slow, since these algorithms are only for narrow-phase collision detection.
enn0x