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Sunflower HexChess

Introduction

I was browsing the web on the subject of "tessellating the Euclidean Plane" when I came across this page on hexagonal tessellations.  Hexagons and hexagonal chess variants hold a certain fascination for me and I was particularly drawn to the radial tessellation centred on an octagon.  Serendipitously I had also just been reading about Circular Chess, and so was born the idea of creating an hexagonal variant with a circular motif. 

Due to the increasing number of cells rather than an increasing size of cells, as we move outward on the board, the resulting game might be better termed "radial chess" rather than "circular".

Setup

The board consists of 120 hexes, each in one of three colours and each with a border in one of 5 colours.  There are 40 hexagons of each colour.

The  exact colours used for the board cells are immaterial though the images here use three yellowish hues: a pale yellow; a golden yellow; and a dark greenish yellow.  The five border colours help in defining the topology of the board.  Again, the precise colours are irrelevant with the images here using shades of red and brown.

The board reminds me somewhat of a sunflower , hence the name of the variant.
the 5 tracks start array
The 120 hexes are arranged in five paths or tracks that encircle the central octagon and the cells in each path have the same colour border.  These paths are illustrated by the image above-left.

The inner path consists of 8 cells with a light red border.
The mid-inner path consists of 16 cells with a light brown border.
The middle path consists of 24 cells with a red border.
The mid-outer path consists of 32 cells with a dark brown border.
The final 40 cells with a dark red border form the outer path.

Movement around a single track, clockwise or anti-clockwork, is permitted and is classed as orthogonal movement

The image above-right shows the starting position of the pieces. 

Notation

cell reference

As well as being arranged in the 5 tracks, the cells of the Sunflower board can be divided into 8 sectors.  In each of these the 15 cells that make up the sector all have the same alignment.

The image on the left demonstrates how this division into sectors is used to produce the individual cell references. 

Each sector is referred to by a letter, a, b, c, d, e, f, g, or h.  Sector (a) consists of the 15 cells aligned East to West and expands outwards to the West or Left, from White's perspective.  The remaining sectors are labelled from Sector (a) in a clockwise direction.

Each sector has a prime radial of 5 cells, one on each track, running from the centre to the outer path. 
These cells, starting from the centre, are assigned a letter, v, w, x, y, and z.

Finally there are up to 5 cells running clockwise along each path from one prime radial to the next.  These "path segment" cells are numbered clockwise from 1 to 5.

Each cell reference thus consists of exactly 3 characters, the sector letter followed by the prime radial letter followed by the path segment number.  These individual cell references are also shown in the left-hand image.

At the start of a game the white pieces occupy all of sector {g} plus the prime radial of sector {h}.  The black pieces occupy all of sector {c} plus the prime radial of sector {d}.



Pieces

Orthogonal and Diagonal Movement

Adjacent Cells
adjacent cells
Series of steps
Series of steps
Moves consist of a series of either orthogonal or diagonal steps.  The top image on the right shows the cells adjacent to the hex labelled "S".  Those marked "o" are reached by a single orthogonal step; those marked "d" by a single diagonal step.

An orthogonal step is taken from the current cell to an adjacent cell joined along a cell edge.
A series of orthogonal steps must conform to the following rules.
  1. The first step will cross two borders of either the same colour or of differing colours.  Subsequent steps must follow the pattern set by the initial step in respect of the borders.  Thus if the first step crosses same-colour borders, any subsequent step forming part of the same move must also cross same-colour borders.  This will be the case when a piece is moved along one of the five tracks.
  2. When the series of steps crosses different-colour borders, the exit edge from a hex must be directly opposite the entry edge.
A diagonal step is taken from the current cell to an adjacent cell connected through a cell corner and will always be between hexes of the same colour.  The border colour does not affect diagonal movement.  In a series of diagonal steps the exit corner from a hex must be directly opposite the entry corner.  Possible step series are shown in the bottom image on the right.

The red dots form a diagonal series while the blue (same-colour borders) and green (different-colour borders) form two orthogonal series.  Note that the cell marked by a green cross cannot form part of  the green dot series.

Piece Movement

pawn icon

Pawn - each player starts with 10

pawn moveMoves by advancing up to a maximum number of hexes along an encircling path.  The maximum number depends on the path:
      • inner path - maximum 1 hex
      • mid-inner path - maximum 2 hexes
      • middle path - maximum 3 hexes
      • mid-outer path - maximum 3 hexes
      • outer path - maximum 4 hexes
Captures by advancing 1 hex into an adjacent track across either the inward or outward forward facing edge.  Capturing "en passant" is not permitted.

White pawns that start on the h prime radial and Black pawns that start on the d prime radial advance clockwise: all other pawns advance anti-clockwise.

Pawn movement and capture is demonstrated by Pawns A to F in the image on the right.

Pawns must promote when they end their movement beyond the nearest line of hexes from which the opposing pawns start.  In the image the promotion hexes for clockwise-moving White pawns are marked by green dots.

bishop icon

Bishop - each player starts with 3

bishop moveMoves or Captures by sliding any number of hexes along a diagonal but may not jump over other pieces.

May capture an enemy piece that is the first piece along the line of movement.
rook icon

Rook - each player starts with 3

rook moveMoves or Captures by sliding up to a maximum of six hexes along an orthogonal but may not jump over other pieces.

May capture an enemy piece that is the first piece along the line of movement and which is within the maximum number hexes allowed.

dragoon icon

Dragoon - each player starts with 2

dragoon moveMoves 1 hex in any direction into an empty adjacent cell.  It may not capture when moving just a single step.

Moves or Captures by leaping 2 or 3 hexes in any direction.  It cannot be blocked by any intervening pieces.

In the image on the left the hexes where captures are possible are shown by the red dots.
queen icon

queen moveQueen- each player starts with 1

Combines the moves and captures of Rook and Bishop
king icon

King- each player starts with 1

king move
Moves 1 hex in any direction. 

Cannot move into a hex that is attacked by an opponent's piece.



Rules

The two sides are White and Black, moving alternately with White moving first.

Each player starts with 20 pieces:
10 Pawns, 3 Bishops, 3 Rooks, 2 Dragoons, 1 Queen, 1 King.


A player wins if:
  1. The opponent's King is checkmated.
  2. The opponent is left with only a King, all other pieces having been captured.
  3. The opponent is unable to make a legal move (stalemate).
  4. The opponent's last move causes the third repetition of a position.


Notes

Although partly inspired by Circular chess this variant is not an attempt to create an hexagonal equivalent of that game.  Rather it is an attempt at using a delightful hexagonal tessellation as the basis for a game board.  Any attempt at transferring the circular game into an equivalent hexagonal format would need at least to keep the same number of cells in each encircling ring, rather than the increasing number as seen here.

This increasing number of cells, with 40 hexes in the outer track, is the main reason for the restriction on orthogonal movement as I wanted to maintain a balance between the strengths of bishop and rook.  As the longest diagonal and the longest non-path orthogonal is 5, a maximum move of 5 hexes might seem the obvious choice.  However I wanted to keep the rooks slightly stronger than the bishops as is the usual case in chess.  On a board with hexagonal cells increasing the obvious 5 to a maximum of 6 seemed appropriate.

The length of the outer tracks also explains the  enhanced pawn movement.  Without the  increase  in  movement  allowed to the pawn on the outer paths progress from starting position to promotion would be just too slow.

I was also unhappy with the knight's move on a board which is effectively quite narrow and which thus prevents a knight from achieving it's maximum move potential.  So I devised a leaping piece better adapted to the board's topology to replace the knight, which I have called a Dragoon.  Originally dragoons were mounted infantry, able to defend a position or ride to the point of conflict before dismounting to fight on foot.  So the Dragoon is able to move, but not capture, by stepping 1 cell in any direction, or move and capture by leaping 2 or 3 cells in any direction.  The icon used here for the Dragoon is the orthodox knight backed by a pair of crossed cavalry sabres.

Playing Tips

Fool's Mate

Checkmate by White is possible in just 2 moves, as illustrated by the following images

fools mate 1
fools mate 2 fools mate 3
1. Dragoon gz5 - hz3
1... Bishop cx2 - bz1 2. Dragoon hz3 - fv1 #

Relative Piece Values


Pawn
Bishop
Rook
Dragoon
Queen
Suggested value
1.0
3.0
4.5
6.0
7.5



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By Graeme C Neatham.
Web page created: 2006-12-22. Web page last updated: 2006-12-22