The Chess Variant Pages

Check out Expanded Chess, our

featured variant for September, 2023.

[ Help | Earliest Comments | Latest Comments ]
[ List All Subjects of Discussion | Create New Subject of Discussion ]
[ List Latest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]

Comments/Ratings for a Single Item

Later Reverse Order EarlierEarliest
Penturanga. Chaturanga on a board with 46 pentagonal cells. (8x5, Cells: 46) [All Comments] [Add Comment or Rating]
Ben Reiniger wrote on 2010-08-26 UTC
So this is really (locally) a hexagonal game, since each 'square' has six neighbors; is it different (globally) from a standard hex setup?

EDIT: Ah, I missed this discussion a couple years back.  I think perhaps the original comment by Gilman answers my question most fully: it's not a 'standard' hex setup.  It seems too that the piece movement is not standard for hex games, but I don't see anything that forces us to use the pentagonal layout for ease of visualization.  It is neat though how the pentagons have been laid out.

Daniil Frolov wrote on 2010-08-26 UTCGood ★★★★
Actually, representation is everything. For example, look at my game 'Square and hex on same board' -
or at this (zzo38) A. Black's comment about 1-dimensional games -

But i'm going to post another petagonal variant now, wich is more different from hexagonal variants, each 'square' have 5 orthogonally-adjecent 'squares'.

Joe Joyce wrote on 2008-12-10 UTC
Yes, the horses are 'colorbound'; they travel a circuit that only includes 1/3 of the board, like the elephants. Unlike the elephants, the knights not only change pentagon colors while traveling, they form pairs with their diagonally opposite opponent horses, so they are able to be exchanged, whereas only one pair of opposing and exchangeable elephants exists. Note that exchanges between elephants and knights exist and are balanced. The weak pieces, able to visit only limited portions of the board, and not necessarily able to interact with each other, are a feature of the oldest games of chess. Graeme's subtle use of this contributes to the 'large' feel of a small game, and it is not easily noticed. Nice eye. Did you notice it while looking at the 3x5 hex board? The pattern should show up more strongly there. It's easy to miss the boundness, as the knight's move is the easiest to do wrong in a game.

John Smith wrote on 2008-12-10 UTC
I'm just saying, if you want a third Elephant. Does anyone notice that the Horses are colourbound?

Joe Joyce wrote on 2008-12-09 UTC
John, you're right that modifying the board that way gives an extra rear rank board location for each side to place a third bishop, and, being 3 pentagons per hexagon, this also gives a 45 position board, fitting the contest theme. I have 2 objections to that, however, The first is aesthetic. The board will be a parallelogram, with corner angles of 60 and 120. It doesn't look right, and it's annoying to play at an angle like that - you want to grab the board [right off the screen] and straighten it out. The second objection is concerned with playability. 

Take a look at both of the boards. The center row of one is 3 hexes - 9 pentagons - across. The other is 4 hexes, and 12 playable spots in the middle of the board. The 3 extra spots in the center on Graeme's board are the one that was lost going from 46 to 45, and the two that the extra elephants occupy, now in the back rows. Does this make much of a difference?

How many pawns does it take to make a solid wall completely across the board? In Graeme's game, in the setup, the 6 pawns cover the 3 hex board 'row' they're on, occupying 2 of the 3 pentagons in each hexagon. To do the same in the middle of Graeme's, you'd need 8 pawns, which the game doesn't have. The middle of Graeme's board cannot be clogged by pawns. On the 45 position board, it only takes 5 pawns to clog [form an unbroken line from side to side] the board. There are 6 pawns in the game. 

In general, especially with all other things being equal, I believe that the narrower the front, the easier it is to jam it up with pieces and kill zones, so the more drawish it will be. Further, Graeme's board is very roughly circular [at least in intent], giving maximum room for maneuver in the center of the board. This game won the contest because it 'plays big'. It feels like the 64 square game, even though it's on a much smaller board. It also doesn't feel crowded, thought the starting piece density is ~60%. Narrowing the board from Graeme's 6-8 pentagons down to 5 pentagons, losing one spot and adding two pieces would likely create a clog in the middle of the board, in my opinion.

John Smith wrote on 2008-12-09 UTC
Graeme, did you think of making a board with 3 columns by 5 rows of hexagons? Doing so allows you to have 3 Elephants without an awkward setup.

💡📝Graeme Neatham wrote on 2008-11-29 UTC

Sam Trenholme wrote:
'Would you be open to me modifying your Zillions' file ...'

Please feel free to modify the file as you wish.

I think Game Courier only supports square or hex boards though it may be possible to upload a custom graphic.

Sam Trenholme wrote on 2008-11-29 UTC
Mr. Neatham:

Would you be open to me modifying your Zillions' file to have, in the variant pop-down-list, some ideas suggested here:

  • Free pawn promotion
  • An opening setup where each side gets three elephants
  • Both of the above ideas
If so, I can make the necessary changes to the Zillions file. Also, I wonder how hard this will be to implement for Game Courier.

- Sam

John Smith wrote on 2008-11-28 UTC
I would be interested. I could help you make a game out of that idea if you'd like. I'm very good at making games with a certain attribute or restriction.

Sam Trenholme wrote on 2008-11-28 UTCExcellent ★★★★★
I love it when people break the mold and come up with an alternate tessellation for a chess variant (such as Parachess).

Speaking of which, is there any interest in my inventing a variant using an alternate tessellation. I have an idea that has been bouncing around my head for over a decade which I should make a variant out of, but only if people would be interested in looking at it.

- Sam

John Smith wrote on 2008-11-28 UTCExcellent ★★★★★
This game is great. I have 2 complaints, however. 1 is that there is a bias for the medium tan for the Elephant's boundness. Perhaps you could change the setup and have 3 Elephants per side. 2 is that the board is too cramped, just as in your other game, Step and Circle Trig Chess.

JCRuhf wrote on 2008-07-17 UTCGood ★★★★
I like this game very much, but I would not have limited the pawn promotion
so much had I created it. The first thing I would do if I were
transliterating Chaturanga/Shatranj to a quasi-pentagonal board would be
to keep the basic pawn promotion rule from the original game intact
instead of discarding it altogether and then add the piece that starts on
or directly in front of that cell to the promotion options. In the event
that a Pawn landed where the opponent's Adviser/Counselor started, it
would be able to promote to any piece other than the king. That gripe
aside, the game is a very good quasi-pentagonal version of chess. However,
there is no rating between Good and Excellent and I could not really give
an Excellent rating the game is not completely faithful to its historical
original with regards to Pawn promotion.
P.S. I am referring to the board as quasi-pentagonal because a true
pentagonal board is a tessellation of pentagons that does not involve
pushing small groups of them together into shapes other than pentagons and
I did not call it hexagonal as that would imply that it was nothing more
than a hexagonal grid.

💡📝Graeme Neatham wrote on 2007-12-08 UTC
just sent you an email.


Joe Joyce wrote on 2007-12-08 UTC
Graeme, sorry for contacting you this way, but I've had some computer issues recently, and I currently cannot send emails, though I can receive them.

Do you have board templates for this game and your other contest entries? If you do, would you please email them to me [see my person info onsite], as I'm lazy enough [or too pressed for time right now, if you prefer] not to want to make the boards tonight or tomorrow morning, for purposes of judging your entries. Jeremy and I hope to look at them this weekend, as we've already started work on the entries. We got together a bit last weekend and looked at 2 games [not yours], and plan to get together after this weekend at least once more in January to continue the difficult work of playing games to see which ones are best; rough, but somebody's gotta do it. If you don't, no big problem. By next month, we can make the boards, and look at your stuff then. Either way, thanks for your attention to this. Joe

David Cannon wrote on 2007-12-04 UTCExcellent ★★★★★
Well done Graeme! I like this layout. One suggestion I'd make is to expand the board, however. The size is ideal for the short-range pieces, but the rook would love some long runways to run on. I'm impressed by the way you've been able to design a pentagonal board; I've tried that myself, but couldn't come up with a model that satisfied me completely. But you've done it - congratulations.

Jonathan wrote on 2007-12-04 UTC
It does appear that this game visually lends itself to different kinds of
movements, even if it can be seen as an equivelent to a hexagonal board. 
For instance a rook piece may alternate between one and two paths to reach
a destination cell.

 / \     / \
| - \_-_/ X |
| - / - \   |
 \ /_____\ /

In the lame ASCII diagram I have just given, you can see how a rook on the
far left pentagon can take two routes to reach cell X (the hyphens
representing arrows outlining the two paths).  If I had the
patience to produce another set of pentagons, you could see how both paths
merge on X, but could then split and merge over and over again.  Though
this movement is equally possible on a hex grid, it is far more visually
appealing on Neatham's Pentagonal grid.  I think that it could even be
interesting to allow the rook to change which path it takes whenever
desired, making it a difficult piece to block.  I believe further
exploration of Penturanga's idea could be quite interesting


Perhaps a better pentagonal grid would have been a more pure one in
nature, like the one shown here:

This grid only allows its pentagons to come in contact edge-to-edge five
times.  This may be the more pure grid that some here are seeking.

Gary Gifford wrote on 2007-12-03 UTC
Hi Graeme: Congrats on what appears to be a nice and very clever game. Thanks for pointing out where the pieces came from. I was thinking I saw them in a computer program, though perhaps it was only here at CV. Anyway, clever job... and clever pentagons.

Doug Chatham wrote on 2007-12-03 UTC
The old CVP-linked pentagonal game that you mentioned, is it Webball, which is played on a dodecahedron?

George Duke wrote on 2007-12-03 UTCExcellent ★★★★★
Or are all the hexagonal variants ''funny-looking'' pentagonal ones? Ralph Betza's Rectahex Chess (2003) concludes ''Hexagonal Chess can be played quite simply on normal rectangular board.'' Betza's resolving hex dynamics there worsens visualization, but Rectahex is excellent for Betza's satiric, clever transformation. This Penturanga marginally improves ease of visualizing interpretatively-hex movements, in acceptable technique for claiming novelty at sophisticated stage as this, pursuant thousands of forms. Differently -- hey, there are hundreds hexagonal chesses, so why not a hundred pentagonal ones -- US Patent No. 4357018 [Go to USPTO 'Number Search'] 02.Nov.1982 to Murray Calvert, of London, Ontario, Canada, has CV of ''interlocking chains of regular pentagons in side by side abutment,'' intended for play of Chess, Checkers and Dominoes. So, Charles Gilman's ''board of genuine pentagons'' has been done before. Another one US Patent No. 3981505 ''Irregular Pentagons'' 21.Sept.1976 to Marc Odier, Paris, France, is more puzzle-mechanism device than actual CV. It improves on Odier's prior USP3608906 28.Sept.1971 and France Patent No. 1582023. Another one 14.August.1883 (125 years back) USPatent 282990 to Percy Johnson, Marlborough, Mass., USA, also has chess embodiment played on pentagonal spaces. Chess Variant Page also linked a Pentagonal chess several years ago I cannot find right away. What goes around comes around.

💡📝Graeme Neatham wrote on 2007-12-03 UTC

Your example piece is a red herring.

My example piece may well be called a herring, red or otherwise, but it illustrates that topological equivalence, though necessary, is not sufficient for game equivalence. That having been said, I agree that for the pieces actually used in Penturanga there is game equivalence between the pentagonal and the hexagonal boards.

... but this is a mathematical problem with a definitive answer.

Exactly! A square has 4 sides, a hexagon has 6 sides, a triangle 3 sides, and a pentagon 5 sides. A board with 6-sided cells is termed hexagonal, so surely it is correct to term a board with 5-sided cells pentagonal?


Pythagoras wrote on 2007-12-03 UTC
Your example piece is a red herring. And as far as 'I'm afraid that is not a fact, it is, like mine, just an opinion - so may we just agree to differ?' I guess we can agree to stop debating, but this is a mathematical problem with a definitive answer. Not everything is a matter of opinion despite the current proliferation of relativism. Thanks for the other fine variants.

💡📝Graeme Neatham wrote on 2007-12-03 UTC

'Topological equivalence also does not lead to equivalence in game-mechanics.'

Create a piece whose move is defined as:

a series of steps away from the starting cell exiting each cell via a short side.

Such a piece can be moved on the Penturanga board but not on the topologically equivalent hex-board.

'...the fact remains that Penturanga is just a funny-looking hexagonal chess variant.'

I'm afraid that is not a fact, it is, like mine, just an opinion - so may we just agree to differ?


Pythagoras wrote on 2007-12-03 UTC
Despite the gruff tone of my last comment, I found some of Mr. Neatham's
other games to be good efforts: Fool's Hex Chess, A9, TriMac HexChess,
and Penguins and Predators.

Pythagoras wrote on 2007-12-03 UTC
'Topological equivalence also does not lead to equivalence in

Oh yes it does.

'In short it is my opinion that Penturanga is indeed truly pentagonal.'

Regardless of your opinion, the fact remains that Penturanga is just a
funny-looking hexagonal chess variant.

💡📝Graeme Neatham wrote on 2007-12-03 UTC

Thank you all for taking the time to examine and comment on Penturanga.

Charles, I'm not sure exactly what you mean by 'despite the presentation', but I admit it to be somewhat sparse. In order to meet the competition deadline I published the basic description without a supporting Notes section. I hope to add this and publish a zrf shortly.
Also , while I agree with you that that the board is topologically equivalent to the hex-board you describe, this does not mean the pentagons are anything else other than pentagons - the number of surrounding cells is irrelevant as can be seen by the usual square board where each cell is surrounded by 8 others. Topological equivalence also does not lead to equivalence in game-mechanics. In short it is my opinion that Penturanga is indeed truly pentagonal.

Gary, the piece graphics were derived from a Chinese set published on this site. Full accreditation will be given in the Notes.

25 comments displayed

Later Reverse Order EarlierEarliest

Permalink to the exact comments currently displayed.