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I have noticed some pages in this site (I forget which ones) described the 'hippagonals' as 'the lines halfway between diagonals and orthogonals'. They are not. The hippagonals are at inverse tangents of -2, -.5, .5 and 2 from forwards, which are at about 26.6 degrees from the orthogonals (18.4 degrees from the diagonals). The lines halfway between the diagonals and orthogonals are 22.5 degrees from each, and will not cross the centres of any squares no matter how big a board they are on.