Hello,
Consider the following ellipsoid in R^n
x_1^2/a_1^2+x_2^2/a_2^2++x_n^2/a_n^2 = 1
( can assume a_i <= a_j for i < j without loss of generality)
I am interested in finding out a regular simplex (equilateral triangle
in 3D, regular tetrahedron in 4D etc) on this surface. While I have an
intutive idea as to how the points could be placed on the surface of
the ellipsoid to form a regular simplex, I was wondering if there is a
closed form formula for these points. Any pointers on related work in n
dimensions will be appreciated. It turns out to be very trivial in 2D.
Thanks