There are three points on the surface of a sphere centered at origin. One has an x coordinate of 0, another has a y coordinate of 0, and the last has a z coordinate of 0.

What is the biggest possible equilateral triangle that can be made using these three points as the corners? How many equilateral triangles of this size are possible?

What if instead of a sphere, it is a regular octahedron centered at origin, with each of its vertices on an x, y, or z axis?

(In reply to part 1 spoiler by Charlie)

The way I interpreted Tristan's problem, all three points must be used as the three corners of the triangle, not one point at a time.  I see only one solution, an equilateral triangle with sides r*sqrt(2); Area = (r^2)*(sqrt(3)/2).  The same triangle would be the face of the regular octahedron (d8).

Posted by MindRod on 2005-12-05 22:18:29