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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:

A-A-A-A-A-A-A-A
-B---C---C---B-
---D-------E---
-------F-------

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?