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PUNNING BY NUMBERS

A Systematic Set of Names for non-coprime radial pieces

Charles Gilman

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Credits

Author: Charles Gilman.

Comments

Punning by Numbers. A systematic set of names for cubic-cell oblique pieces.

Charles Gilman wrote on Fri, May 26, 2006 02:27 AM EDT:

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.

Charles Gilman wrote on Tue, Jan 24, 2006 09:01 AM EST:

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.

Mason Green wrote on Fri, Mar 18, 2005 06:38 PM EST:

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 03:22 AM EST:

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 04:38 AM EDT:

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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First Created: Saturday, August 28th, 2004
Last Modified: Thursday, November 9th, 2006
File Timestamp: Wed, 14 Jul 2021 17:37:29 -0400
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