What are the vertices of a regular tetrahedron embeded in a sphere of radius R Imagine you had a sphere of radius R centered at the origin.  What are the coordinates of the vertices of the regular tetrahedron which is circumscribed by the sphere?  One of the vertices of the tetrahedron is (0,0,R) and one of the vertices lies in the z,x plane.

The tetrahedron coordinates:


*

*(0.000, 0.000, 1.000)

*(0.943, 0.000, -0.333)

*(-0.471, 0.816, -0.333)

*(-0.471, -0.816, -0.333)


Length of every edge: 1.6329932 
Of course, the real answers have square roots in them. You can scale by the radius.
