I am using Paraview 5.10.0-RC1 and want to apply the Cell Size filter. This returns a negative value of -1/6 for the tetrahedral volume. Is there is a specific reason for this volume being negative?

Is there is a specific reason for this volume being negative?

Yes ! the order of the vertices of the tetrahedra (and any other element) follow conventions to ensure consistency across calculations .
See figure 2 in the documentation .

in this case the normal vector of the face defined by the first three points using the right hand rule, points â€śoutwardsâ€ť, away from the fourth vertex and thus the volume is considered negative.

This is rectified if you change the order of the two last vertices:

The first three vertices define now a normal that points on the same side of the face that [1,0,1] lies.