The spherical tetrahedron ADDD

In this conformal image the yellow sphere is the equator between 1 and -1. We are looking at it from the 1 side, so -1 is at the center. The tetrahedron is positioned with vertices i,j,k,a^2. The four vertices are colored violet; the other group points are colored blue. Here i is at the top of the picture, j is on the left, k on the right and a^2 in the foreground. The group elements -b,-c,-d are the midpoints of the edges ia^2, ka^2 and ja^2 respectively, while the elements b^2, c^2 and d^2 appear on the faces jka^2, kia^2 and ija^2 respectively. The group element -1 is in the interior of this tetrahedron.
This is the largest of all the 12 possible spherical tetrahedra with vertices in the binary tetrahedral group. Its volume, 15/64, is almost 1/2 the volume of a hemisphere.

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