Fellow Engineers, I've been tasked/cursed with learning how these equations were derived, but I was never that good at trigonometry, much less 3d trigonometry that involves transformation. I've checked the literature and most never bother explaining how this was derived and instead just cite the author. This is his paper, here are 2 other reference view points to the unit cell parametrization of the Miura ori structure in question and this paper offer more views by the original author at page 3.
In brief they're unit cell parametrization of a Miura Ori cell before (Lo, So) and after (L, S) folding. The dihedral angle between the planes is theta, gamma is the acute angle between parallelograms. There is a discrepancy between the terms used between the two cited papers, but they're using the same model. I'm not sure whether this is obvious so others dont bother writing it or it's too difficult so they dont bother rederiving them. I can see how H = a sin gamma sin theta, but I'm not sue why how any of the other relations were derived.
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