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What's this 'obliquely orthogonally'? The phrase suggests that you are struggling with hex geometry. A Berolina Pawn's noncapturing move is neither oblique nor orthogonal, and I cannot see how any one-step move can be both.
Clearly you are not versed in Glinski. The Berolina Glinski moves without capturing 60 degrees to the forward part of the vertical axis, and captures forward on the vertical axis. I use the term obliquely just as it is used in the TCVP Glinski's Hexagonal Chess page.
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