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Charles Gilman wrote on Mon, May 3, 2010 06:36 AM UTC:
I have now identified 4 odd integers n for which the cubic board has:
(1) an x:y:z leaper of length root n;
(2) directions of that leaper at right angles to each other;
(3) a dual leaper of length root 2n, resulting from the hypotenuse of two x:y:z leaps;
(4) a resulting leaper of length n, resulting from x x:y:z moves in one direction, y in another, and z in a third;
(5) directions of that leaper at right angles to each other;
(3) a dual leaper of length 2n, resulting from the hypotenuse of two of those leaps.

They are:

n(1)(2)-(3)(2)-(4)(5)-(6)
5Knight[2:-1:0]+[1:2:0]=[3:1:0] Camel2[1:2:0]+[2:-1:0]+0=[4:3:0] Antelope[4:-3:0]+[3:4:0]=[7:1:0] Namel
9Ninja[2:2:-1]+[2:-1:2]=[4:1:1] Nimel2[2:1:2]+2[1:2:-2]+[2:-2:1]=[8:4:1] Ultimatum[4:8:-1]+[4:-1:8]=[8:7:7] Lumel
13Zebra[3:-2:0]+[2:3:0]=[5:1:0] Zemel3[2:3:0]+2[3:-2:0]+0=[12:5:0] Zoetrope[12:-5:0]+[5:12:0]=[17:7:0] Zomel
17Giraffe[4:-1:0]+[1:4:0]=[5:3:0] Gimel4[4:1:0]+[-1:4:0]+0=[15:8:0] Gyroscope[15:-8:0]+[8:15:0]=[23:7:0] Gymel
Given that the name Antelope is fixed it makes sense for the name of the symmetric n coprime leaper to be relatively unconnected to the root-n one's - although I manage to convey a double connection with Zoetrope and Gyroscope. However, it occurs to me that something could be done with forward-only (FO) pieces to make more use of a limited number of initials. For examnple the FO versions of the Antelope/Namel/Anu, currently named Quintet/Qump/Qandyman, could be renamed Haste/Hardness/Heaven (the first indicating fast movement, the second a quality of enamel, the third the sky personified by Anu). The FO versions of the Ultimatum/Lumel/Uluru would then be the Daste/Dardness/Deaven, those of the Zoetrope/Zomel Saste/Sardness, and those of the Gyroscope/Gymel Baste/Bardness. There would however then need to be new names for the FO versions of the Natamaran and Narrier, to replace Qull and Qold.

There would also need to be replacements for Rook+Anu=Qomestead, Bishop+Anu=Qallow, Queen+Anu=Qarridan, and Unicorn+Anu=Qarbinger. At this point it occurred to me that I should yet again rethink the names for compounds of a radial linepiece and an oblique triangulator. There were some ideas that I'd had building on the Ace-Acme pattern. At the time I judged them too vague, but now I can see the advantage of aplying them to semi-dual pairs as well. Thus if the Gnu's Rook/Bishop/Queen/Unicorn compounds, currently the Homestead/Hallow/Harridan/Harbinger, were to become the Acropolis/Actor/Actress/Acuity (last referring to unicorn having sharp horn) this would make things easier as not only would the Nintu's compounds become the Inropolis/Intor/Intress/Inuity and the Zebu's the Ezropolis/Eztor/Eztress/Ezuity, the Antelope's could be the Anropolis/Antor/Antress/Anuity (derived name rather than misspelled real word) but also the Lefanu's the Elropolis/Eltor/Eltress/Eluity and the Feu's the Efropolis/Eftor/Eftress/Efuity. Of course I have already used the Gnu compounds in two variants, so I have to decided to check whether anyone objects to renaming them.

That will still leave the question of what H-names should replace Qull and Qold, so any suggestions for those two are welcome. Others will be needed for the Qaymaker (Fieldmouse+Numbat) and its own FO version the Qillock, prefebly ending with -er and -ock respectively.


Charles Gilman wrote on Mon, May 3, 2010 05:52 PM UTC:
Since the first posting I've realised that Heaven won't do as it has the
wrong ending - the Anu's FO version should end with -an. Headman would
suit the theme, as high rank echoes a literally high sky god such as Anu.
That would make the FO Uluru's derived name Deadman, but one cannot have
everything. I am now toying with Qull and Qold becoming Haggle and Heckle,
to tie in with the overtones of Natter and Narrate in Natamaran and
Narrier, and Qaymaker and Qillock becoming Hedger and Headlock.

Charles Gilman wrote on Wed, May 12, 2010 05:47 AM UTC:
I have worked out a list of possible renamings for this process. I am still
happy to hear any ideas for improvement, or other objections to making the
changes, or answer any queries as to the connections of real-word names
with their components.
	Radial plus Triangulator compounds:
Homestead=>Acropolis, Hallow=>Actor, Harridan=>Actress, Harbinger=>Acuity,
Hustler=>Accoster
	Resulting derived names
Domestead=>Inropolis, Dallow=>Intor, Darridan=>Intress, Darbinger=>Inuity,
Dustler=>Incoster
Somestead=>Ezropolis, Sallow=>Eztor, Sarridan=>Eztress, Sarbinger=>Ezuity,
Sustler=>Ezcoster
Bomestead=>Igropolis, Ballow=>Igtor, Barridan=>Igtress, Barbinger=>Iguity,
Bustler=>Igcoster
Qomestead=>Anropolis, Qallow=>Antor, Qarridan=>Antress, Qarbinger=>Anuity,
Qustler=>Ancoster
Momestead=>Afropolis, Mallow=>Aftor, Marridan=>Aftress, Marbinger=>Afuity,
Mustler=>Afcoster
Uomestead=>Erropolis, Uallow=>Ertor, Uarridan=>Ertress, Uarbinger=>Eruity,
Uustler=>Ercoster
et cetera
	New derived names
Rook+Lefanu=Elropolis, Bishop+Lefanu=Eltor, Queen+Lefanu=Eltress,
Unicorn+Lefanu=Eluity, Dicorn+Lefanu=Elcoster
Rook+Feu=Efropolis, Bishop+Feu=Eftor, Queen+Feu=Eftress,
Unicorn+Feu=Efuity, Dicorn+Feu=Efcoster
Rook+Nunchaku=Unropolis, Bishop+Nunchaku=Untor, Queen+Nunchaku=Untress,
Unicorn+Nunchaku=Unuity, Dicorn+Nunchaku=Uncoster
Rook+Voudou=Ovropolis, Bishop+Voudou=Ovtor, Queen+Voudou=Ovtress,
Unicorn+Voudou=Ovuity, Dicorn+Voudou=Ovcoster
et cetera
	Forward-only squares and their duals:
Quintet=>Haste, Qump=>Hardness, Qandyman=>Headman, Qull=>Haggle,
Qold=>Heckle, Qaymaker=>Hedger, Qillock=>Headlock
	New derived names
FO Ultimatum=Daste, FO Lumel=Dardness, FO Uluru=Deadman, FO
Nutamaran=Daggle, FO Nurrier=Deckle
FO Zoetrope=Saste, FO Zomel=Sardness, FO Zotamaran=Saggle, FO
Zorrier=Seckle
FO Gyroscope=Baste, FO Gymel=Bardness, FO Gytamaran=Baggle, FO
Gyrrier=Beckle

Charles Gilman wrote on Sun, May 23, 2010 06:30 AM UTC:
Well I've gone ahead with the substitutions with which I was most
satisfied: Haste for Quintet, Hardness for Qump, Headman for Qandyman,
Hedger for Qaymaker, Headlock for Qillock, and 12:5 / 17:8 / 8:4:1
extrapolations. I also realised that logically I should substitute Etsah
for Tetniuq, which I have also done.
	I am now, however, having second thoughts about Haggle and Heckle, and am
veering instead to using replacing the Hull/Hold family in its entirety. I
am now looking to rename the Hull the Cabin and the Hold the Caisson (a
wagon for carrying ammunition), as Ca- names can then be extrapolated to
compounds in semi-dual as well as dual directions. These would thus include
Leyline+Lenard=Lebin, Leverage+Lerving=Leisson, Felf+Fenard=Febin,
Fertridge+Herving=Feisson, et cetera as well as Nilf+Ninard=Nibin,
Nirtridge+Nurving=Niisson, Zelf+Zenard=Zebin, Zertridge+Zerving=Zeisson, et
cetera. Qull and Qold would then become Nabin and Naisson. I am still up
for better suggestions should there be any, but I would be surprised.
	Where I am still hopeful of improvement is to Homestead=>Acropolis,
Hallow=>Actor, Harridan=>Actress, Harbinger=>Acuity, Hustler=>Accoster, and
their offshoots. Thoughts on these are especially welcome.

M Winther wrote on Sun, May 23, 2010 07:14 PM UTC:
What are integer leapers?
/Mats

Charles Gilman wrote on Mon, May 24, 2010 06:34 AM UTC:
That's a good point. The subject has got a bit away from its original
title. By 'integer leapers' I meant pieces leaping an exact multiple of
the Wazir's move. For example, the Antelope as a 4:3 leaper moves the same
distace as the 5:0 leaper but in an oblique direction. Of particular
interest to me were those which could be associated with pieces leaping the
root of that distance. You will see from my opening comment that I
expressed 4:3 as 2:1 squared, 12:5 as 3:2 squared, 15:8 as 4:1 xquared, and
in 3d 8:4:1 s 2:2:1 squared. I ignored 8:6 as 3:1 squared as only trivially
distinct from the first. Now that I have completed the changes most
directly based on these relationships, should I move the discussion to a
new thread?

Charles Gilman wrote on Fri, Jun 25, 2010 06:00 PM UTC:
I'm now looking at renaming the Knight/Camel plus Antelope/Namel compounds (clarification - though not the Gnu, which is fixed, or the Anu, with which I am happy) with a view to extrapolating to other compounds involving an integer leaper, its root leaper, and their duals. It's one way of losing Stampede, at any rate, although I'll be disappointed to drop Goum so soon.

Charles Gilman wrote on Sun, Jun 27, 2010 06:26 AM UTC:
My latest thoughts on the pattern is to transfer the current names from
Antelope compounds to Epoletna ones. The names that I am now looking at
are:
	Knight+Antelope=HOVERCRAFT - a fast marine vessel starting with H.
	Camel+Antelope=HAJJ - the pilgrimage not the pilgrim, to give a distinct
ending.
	Helm+Haste=HOTSPUR - the idea of a horseman in armour spurring his horse
on.
	Hump+Haste=HARDSHIP - a property of many a pilgrimage.
	Knight+Namel=COHAJJ, Camel+Namel=COHOVERCRAFT, Helm+Hardness=COHARDSHIP,
Hump+Hardness=COHOTSPUR - derived names.
	Knight+Epoletna=SLEIPNIR, Camel+Epoletna=GOUM, Helm+Etsah=STAMPEDE,
Hump+Etsah=WAVE - reused names, specific to 3d boards.
	Knight+Pentagram=COGOUM, Camel+Pentagram=COSLEIPNIR, Helm+Shilling=COWAVE,
Hump+Shilling=COSTAMPEDE - derived names, specific to hex 3d boards.
	For compounds of 3 or more oblique leapers I never established either
distinct endings or forward-only names, so for Knight+Camel+Antelope+Namel
(alias Gnu+Anu, Hovercraft+Cohovercraft, Hajj+Cohajj) I go one up
(literally up!) from Hovercraft with HELICOPTER.

Charles Gilman wrote on Mon, Jun 28, 2010 08:23 AM UTC:
Derived names in other sets of SOLLs will be:
	Ninja/Nimel+Ultimatum/Lumel=DOVERCRAFT/DAJJ/CODAJJ/CODOVERCRAFT
	Disguise/Dump+Daste/Dardness=DOTSPUR/DARDSHIP/CODARDSHIP/CODOTSPUR
	Ninja+Nimel+Ultimatum+Lumel=DELICOPTER
	Zebra/Zemel+Zoetrope/Zomel=SOVERCRAFT/SAJJ/COSAJJ/COSOVERCRAFT
	Stripe/Sump+Saste/Sardness=SOTSPUR/SARDSHIP/COSARDSHIP/COSOTSPUR
	Zebra+Zemel+Zoetrope+Zomel=SELICOPTER
	Giraffe/Gimel+Gyroscope/Gymel=BOVERCRAFT/BAJJ/COBAJJ/COBOVERCRAFT
	Blotch/Bump+Baste/Bardness=BOTSPUR/BARDSHIP/COBARDSHIP/COBOTSPUR
	Giraffe+Gimel+Gyroscope+Gymel=BELICOPTER
Thoughts of these sets of SOLLs are also turning my attention toward
remaining compounds between pieces with prime and twice-prime SOLLs and
pieces with the square SOLL and/or its dual. Symmetric-piece names that I
have devised include Ninja+Opossum=OPHIR (a city named in Masefield),
Nimel+Opossum=OPPROBRIUM, Elf+Eloper=ELIXIR, Lecturer+Eloper=ELYSIUM. I may
eventualy add Fortnight+Heptagram and Fortnight+Hemel ones too. However, I
am stuck for ideas for -ede names for Disguise+Soaper and Cloak+Ladder, and
-ave ones Dump+Soaper and Oration+Ladder, so any ideas for alternative
endings are still welcome. I assume that there is unlikely to ever be a big
enough 3d board for the likes of Arbez+Zoetrope and Fencer+Gyroscope.
	I have recently been wondering whether to give three-component oblique
pieces distinct endings, but that would involve new changes. For example, I
would have to choose replacements for Bushido and Hidalgo to avoid a clash
with the fixed buffalo. Any ideas on those?

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