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Punning by Numbers. A systematic set of names for cubic-cell oblique pieces.[All Comments] [Add Comment or Rating]Now that the FO Ibex has changed from Juncture to Ledge, I have accordingly changed the FO Isis from Puncture to Pledge, and have submitted an update to this effect.
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.
What's interesting about 3D elemental leapers as opposed to 2D ones is there's a lot more diversity. In two dimensions, each (n:n) or (n:0) leaper has 4 possible destination squares on an infinite board, arranged like the vertices of a square. (n:p) leapers (where n and p are not zero or the same) have 8, forming an octagon. Finally, chiral (clockwise or counterclockwise) versions of the (n:p) leapers have 4, arranged like a rotated square. A 'clockwise' knight can only move to four out of the eight of a full knight, evenly spaced in a clockwise pattern. In three dimensions, we have many leapers whose potential destinations resemble Platonic and Archimedean solids: (0:0:n) 6 destinations, arranged like the vertices of an octahedron. (0:n:n) 12 destinations, forming a cuboctahedron. (n:n:n) 8 destinations, forming a cube. (n:n:p), w/p>n 24 destinations, forming a rhombicuboctahedron. (n:n:p), w/p<n 24 destinations, forming a truncated cube. (0:n:p) 24 destinations, forming a truncated octahedron. (n:p:q) 48 destinations, forming a truncated cuboctahedron. And if that wasn't enough, there's MORE! It is possible to cut the movement possibilities of an (n:p:q) leaper in half, by taking every other destination away to form a chiral leaper (see above) who has 24 destinations, arranged like a snub cuboctahedron. So there are 3 different fundamental 'types' of leapers in two dimensions, and 9 in three dimensions.
Charles Gilman wrote on Mon, Nov 15, 2004 08:22 AM UTC:This article is now correct. The article covering the Zombie is now also up, as The Heavy Brigade.
Charles Gilman wrote on Sun, Aug 29, 2004 08:38 AM UTC:The 28th August posting is based on a submission dating back to May. As it seemed to have been lost, I resubmitted it with several changes. Sorry about the confusion. For the record until everything is sorted out, the following pieces have been renamed: Coordinates Symmetric Forward-only 5:5:2 Expounder Tale 7:2:1 Propounder Rant 6:5:1 Endower Rite 7:3:2 Avower Fate
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