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