[maka]

(1) if we change blockMeshDict to: (see the end of the message)
(2) run blockMesh and then checkMesh
(3) we get from checkMesh:
Mesh non-orthogonality Max: 45 average: 36.4151
(4) I expected :
Mesh non-orthogonality Max: 45 average: (2/3)*45=30.
since 1/3 of the mesh hax non-othogonality=0 (faces normal to z directions).

--------------------------
convertToMeters 0.1;

vertices
(
(0 0 0)
(1 0 0)
(2 1 0)
(1 1 0)
(0 0 1)
(1 0 1)
(2 1 1)
(1 1 1)
);

blocks
(
hex (0 1 2 3 4 5 6 7) (5 5 5) simpleGrading (1 1 1)
);

...

[maka]

case: cavity; V 1.3;

[mattijs]

You are right - to avoid the expensive acos we determine the average in-product, not angle, and only when output convert it into an angle. See primitiveMeshCheck.C::checkFaceOrthogonality.