With configurations jo44 and jo43 we have the first real curvature query where I didn’t already know the answer. With jo44 we have 4 4D simplexes arranged around a 2D bone. All of the edge lengths are 1; they are regular simplexes. Part of the confusion is that these are supposed to be rigid rotations but expressed in oblique coordinates.
The altitude of regular unit side tetrahedron = 2×3−1/2×2−1/2 = (2/3)1/2 = 0.816496580927726 .

In this modification of jo44 the ring of edges around the bone each have length 2/√3 which causes the dihedral angle of the zone at the bone to be 90°. This configuration reports the same result. The calculation seems insensitive to the shape of the zone. This is a bug I think I can find!

For jo44 gij for each zone is 

[| 1.; 0.5; 0.5; 0.5 |] gd
[| 0.5; 1.; 0.5; 0.5 |] gd
[| 0.5; 0.5; 1.; 0.5 |] gd
[| 0.5; 0.5; 0.5; 1. |] gd
which is correct for a regular simplex.

For jo44f it is 

[| 1.; 0.5; 0.5; 0.57735026919 |] gd
[| 0.5; 1.; 0.5; 0.57735026919 |] gd
[| 0.5; 0.5; 1.; 0.57735026919 |] gd
[| 0.57735026919; 0.57735026919; 0.57735026919; 1.15470053838 |] gd
which seems plausible.

We add temporary code to zone.ml to compute the angle between the normals to the two facets that share the bone. These facets are locally numbered 3 and 4 in each zone.

dp = −1 for jo44
dp = −1 for jo44f
Not good. Indeed the dot product of two unit vectors can be −1 only if they are in opposite directions. Both vectors have length 1 (good) and they are not opposites! Back to quadratic forms!!