Math Forum Discussions

Patrick D. Rockwell

Posts: 57
Registered: 12/12/04

Intersection Of Two Simplices
Posted: Dec 20, 2012 2:45 PM

Plain Text

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

Thanks in advance.