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Of A. Black's groupings, the first 3 are radial (the Wazir, Ferz, and
Viceroy of Constitutional Characters) and the 6th is the pieces which are
straight extrapolations of 2d ones (From Ungulates Outwards). Most of the
pieces on this page are of the last group, inevitably including every
triangulator except the Sexton. This leaves the two n:n:p groups as the
most interesting. Pieces named alluding to width (Wideplayer, Feaster,
Expounder, Broadwayman, Wiremaster) are all in the pn group (Longplayer, Dieter) or have
three different coordinates (Propounder, Highwayman, Loremaster) but
always have the longest coordinate greater than the sum of the others. It
may be significant that the one genuine pair of duals comprises the Ninja
(pn). On the other hand unbound, Bishop-bound, and
Unicorn-bound pieces may all be found with two equal shortest
(Fencer/Sexton/Elf), two equal longest (Ninja/Legionary/Underscore), or
three distinct coordinates (Overscore/Fortnight/Oddfellow). Where A.
Black's groupings are perhaps notable is in the Forward-only pieces which
have four directions for two equal shortest cordinates or a zero
coordinate, and eight for two distinct nonzero shortest ones.