While online yesterday morning I caught sight of an image of a genealogy showing a person and their ancestors only, on so small a scale that it could easily have been a Shogi variant camp with twice as many pieces on each rank in a pattern such as:
where the letters are arbitary and no piece has a forward long-range orthogonal move - although B or C might have a forward long-range diagonal move or D or E a forward long-range Knightwise move. It was not however that idea for a square array that inspired me to think further. Instead it occurred to me to have a board with double the numbre of cells per rank, starting with 1. Initially I thought of going up to 16 and having two ranks that size before halving again back to 1, but then I began analysing what sort of cells this generates and I realised that by having just 9 cells on each middle rank I could make all the cells pentagonal. This resulted in the following array:
---------------
| k |
---------------
| q | c |
---------------
| r | n | n | r |
---------------
|p|p|p|p|p|p|p|p|
-----------------
| | | | | | | | | |
-----------------
| | | | | | | | | |
-----------------
|P|P|P|P|P|P|P|P|
---------------
| R | N | N | R |
---------------
| Q | C |
---------------
| K |
---------------
The pieces are the Constrictor, Nadder, Rattlesnake, and Quetzalcoatl as defined in SerPent Chess, together with the Point of Wellisch hex Chess and the King. I rejected using the Boa as it is too weak. Points are promoted to Constrictor, Quetzalcoatl, or Mamba on entering the enemy camp. A Shogi variant would substitute Gold for rhe compound pieces, Silver for Nadder, and Waggle for Rattlesnake, with usual Shogi promotion.
Has anyone got any good ideas for a name for this third pentagonal geometry?
Has anyone got any good ideas for a name for this third pentagonal geometry?