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Topic: Intersection Of Two Simplices
Replies: 0

 Patrick D. Rockwell Posts: 57 Registered: 12/12/04
Intersection Of Two Simplices
Posted: Dec 20, 2012 2:45 PM

Suppose that you have two N Simplices. Call them Simplex A and Simplex B. Both
have an altitude of H and of course are the same size. You inscribe B inside of
A and rotate it so that all of it's vertices are pointed dead center at the n-1
dimensional faces of simplex A. What is the distance in terms of H between an
n-1 dimensional face of simplex A and an n-1 dimensional face of simplex B, both
of which are parallel to each other.

If I'm not mistaken, if n=3, then the answer is 1/2, but what about other
values of n?

also, what is the volume of the intersection.

Finally, can you answer the above if Simplex B has an altitude of 0.9H