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Man and Beast 10: The Hybrid Diagonal. Systematic naming of straight coprime hex-prism-specific radial pieces.[All Comments] [Add Comment or Rating]
Danylo Maschenko wrote on Sat, Dec 16, 2023 06:48 PM UTC:

the 2:1:1:1 is a Foal rather than a Sennight.

You're right! Quite right!

For every two-odds three-distincts cubic leaper there is a 4d one-odds/three-odds one with half its SOLL. By (dual(m:n:o)=((m+n)/2:(m-n)/2:o/2:o/2), where m and n are odd and o is even, the 4d Foal happens to be the cubic Fortnight's dual.

Likewise the pieces corresponding to the cubic 4:3:1 Arbez, 5:2:1 Monk, 5:3:2 Sustainer, 5:4:1 Votary, 5:4:3 Epoletna, 6:3:1 Genome, 6:5:1 Endower and 6:5:3 Dormouse are the 2:2:2:1 Aurochs, 3:2:1:1 Mountie, 4:1:1:1 Student, 3:2:2:2 Offscore, 4:2:2:1 Pentagram, 3:3:2:1 Germinator, 3:3:3:2 Newlywed and 4:3:3:1 Fanatic.


Jerdle wrote on Wed, Aug 2, 2023 01:01 AM UTC:

I have some disagreements with some of the names Gilman has chosen here, and would like to propose my own set, inspired by the existence of this diagonal in 4D hypercubic (in much the same way as the ND exists in 3D cubic and 2D hex).

To start with, the name "Rumchick" is misleading. -chick is the suffix for non-coprime orthogonals. While the FO Rumbaba has the same length as the Dabbaba, it is not one. So, instead, I will return to the pattern theme rejected by Gilman with MALTESE, an eight-pointed cross for the eight forward directions in 4D.

Next up, the World- and Day- pieces are misnamed. They are not generals, but fully symmetric pieces (HD forms of MAB 01 rather than 04). So, in the usual King Queen Prince Princess Princeling order, I will name them OVERLORD, IMPERATRIX, IMPERATOR, PRAETRIX and PRAETOR.

Now we get to the main collection. The augmented Praetors. Gilman names them after the fully-symmetric component, but this leads to the problem mentioned with their riders, so I have continued in the vein of MAB 04 and the lesser generals here.

For the weakest of the four-component generals, I have chosen seasons. WINTER- for Wazir + Sycophant (its similarity to Wazir justifying the theme), SPRING- for Ferz + Dissenter, SUMMER- for Viceroy + Spokesman and AUTUMN- for Rumbaba + Conqueror.

For the strongest generals, I have chosen card suits, using the Latin system (similar to that in Tarot). I would have chosen elements, but Fire- was taken. So Point + Loyalist gets BATON- (weapons of massed loyalists), Cross + Revolutionary gets SWORD- (as in the Crusades), Saltire + Premier gets CUP- (to fit the theme) and Maltese + Archduke gets COIN- (pieces of 8 and connection to power).

For the intermediate generals, I have chosen somewhat arbitrary pairs with some symbolic connection to the components. For those pairing SD with orthogonal, Sky- and Wind- point to AIR- for Prince + Bellboy, while Coast- and Desert- point to EARTH- for Princeling + Bellman. For those pairing ND with orthogonal, Storm- and Forest- point to LIFE- for Duke + Host, while Moon- and Lava- point to DEATH- for Landlord + Count (both somewhat associated with death and evil anyway). Finally, for those pairing HD with orthogonal, Sun- and Fire- point to LIGHT- for Marquis + Heir, while Sea- and Dusk- point to DARK- for Baron + Viscount.


Jerdle wrote on Fri, Mar 10, 2023 05:49 PM UTC in reply to Bn Em from Fri Jan 13 01:40 PM:

Following the MAB 14 definition of a Foal as the next member of the Viceroy-Rumbaba sequence (that is, (0111), (1111)), the (2111) is a Foal rather than a Sennight. There is no Sennight on a tesseract board, the closest equivalent being a Sexton.


Bn Em wrote on Fri, Jan 13, 2023 01:40 PM UTC in reply to Jerdle from 01:47 AM:

This is very true, though a bit out of scope for M&B; while 3D boards seemingly fascinated him, Gilman apparently had no interest whatsoëver in 4D games as they are too far removed from human experience

Fwiw it's not only the Rumbaba (and ofc the Dicorn, Rumchick, extra Generals, ⁊c) that turns up on a Tesseract‐cell board: some of the (in 2‐ and 3D) hex‐specific leapers like the (1,1,1,2) Sennight (or perhaps it's a Foal? here with 64 directions) do too, though I think the likes of the (1,1,2,2) leaper might've needed a new name


Jerdle wrote on Fri, Jan 13, 2023 01:47 AM UTC:

Outside of hex, this diagonal also appears in a 4D tesseract board, in the same way that the 3D ND appears in 2D hex boards. Specifically, the (1,1,1,1) move is a Rumbaba move. The numbers of directions differ though, with WORLD having 80 directions rather than a mere 38.


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