In this conformal image
the yellow-brown sphere is the equator between 1 and -1.
The tetrahedron is positioned with vertices 1,i,j,d.
The four vertices are colored violet; the other group points
are colored blue. Here d is at the top, 1 is on the left, i is at
the bottom and j is on the right.
In this other conformal view, the tetrahedron is positioned
with vertices -1,i,j,-a.