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Man and Beast 14: Oddly Oblique. Systematic naming of hex-specific coprime oblique pieces.[All Comments] [Add Comment or Rating]
Danylo Maschenko wrote on Tue, Dec 26, 2023 10:21 AM UTC:
After a bit of 4d experimentation, it seems that while remaining 2d, hexagonal leapers use a 4-coordinate system rather than a 2- one: one m coordinate, and 3 repeated n coordinates. The latter's repetition could be explained by the Viceroy's SOLL of 3; for every O piece n=0, and for every ND piece m=0. You may have also noticed that some unbound pieces (2:1:1:1 Sennight, 2:2:2:1 Aurochs, 4:1:1:1 Student) have a Viceroy-bound one with thrice their SOLL (2:2:2:3 Overscore, 6:1:1:1 Barnowl, 4:4:4:3 Bettong). This is no coincidence, as if they are both a:b:b:b and c:d:d:d leapers respectively, then c:c:c = b3 and d = a:a:a; in fact you could compare this to the "relative multiplication" system on square boards, where moving an a:b leap c times in one direction and d in the other, as if you were moving a rotated+upscaled Wazir to a specific leap, the final distance passed will be (a²:b²)*(c²:d²). The earliest instance of oblique SOLL-sharing can be seen with the 8:3:3:3 Zemindar and the unnamed 5:5:5:4, both Sennight*Aurochs pieces.