Smooth Modifier lines askew?

I make a box 4x4x4 sections. I apply the smooth modifier. Why are some of the lines askew?
SmoothModifier1.gif
 
That looks indeed "buggy", because
when you take a 1:1:1 box, made editable, apply 2 linear subdivision add Smooth-modifier it looks OK
or take a 1:1:1 box, add Subdivision-modifier (Iterations: 2, Scheme: linear) make editable and add Smooth-modifier it looks OK.
And it seems a Triangulate-modifier will disable Smoothing at all in this set-up: Box 4:4:4+Triangulate-+Smooth-Modifier.
SmoothOperator.jpeg

I´m sure Martin has an explanation.

Cheers
Frank
 
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