more thoughts about SquareHex

Public forum discussion.

#1 · Thomas Werner

5 Oct 2012

Hi,

I found MJongo's thread about SquareHex really interesting and decided to dig a little bit deeper into the connection to Hex boards.

I also thought about a SquareHex board without a field in the center (e.g. based on a Hex board with an even length of sides).

It turns out that you can modify a Hex6 board (as example for all Hex boards with an even length of sides) in two ways. The first one leads to the SquareHex3 board, which can be obtained by modifying the Hex5 board already. The second one leads to a board similar to a SquareHex4 board, but the 5 fields in the middle are replaced by 4 fields (which have an asymmetric connectivity).

By making the second one symmetric one obtains a SquareHex4 board with the center removed. See the boards below for comparison.

Hex boards without a center can end in a draw.

I would really like to see SquareHex on LittleGolem. Maybe SquareHex7 or SquareHex10 games could be internally represented as Hex13 or Hex19 games (possible moves, winning condition, etc).

#2 · Thomas Werner

5 Oct 2012

Hex5 board

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/ \_
\_/ \_
/ \_/ \_
\_/ \_/ \_
/ \_/ \_/
\_/ \_/ \_/
/ \_/ \_/
\_/ \_/ \_/
/ \_/ \_/
\_/ \_/ \_/
  \_/ \_/
    \_/ \_/
      \_/
        \_/

#3 · Thomas Werner

5 Oct 2012

modified Hex5 board

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/ \_
\   \_
/     \_
\    _/ \_
/  _/ \_/
\_/  _/ \_/
/ \_/ \_/
\_/ \_/ \_/
/ \_/  _/
\_/ \_/   /
  \_/
    \_    /
      \_
        \_/

#4 · Thomas Werner

5 Oct 2012

SquareHex3 board

o=====o=====o=====o
I     I     I     I
I  o==o==o==o==o  o
I  I     I     I  I
o==o  o==o==o  o==o
I  I  I     I  I  I
I  o==o     o==o  I
I  I  I     I  I  I
o==o  o==o==o  o==o
I  I     I     I  I
I  o==o==o==o==o  I
I     I     I     I
o=====o=====o=====o

#5 · Thomas Werner

5 Oct 2012

Hex6 board

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/ \_
\_/ \_
/ \_/ \_
\_/ \_/ \_
/ \_/ \_/ \_
\_/ \_/ \_/
/ \_/ \_/ \_/
\_/ \_/ \_/
/ \_/ \_/ \_/
\_/ \_/ \_/
/ \_/ \_/ \_/
\_/ \_/ \_/
  \_/ \_/ \_/
    \_/ \_/
      \_/ \_/
        \_/
          \_/

#6 · Thomas Werner

5 Oct 2012

first modified Hex6 board

_
/ \_
\   \_
/     \_
\       \_
/      _/ \_
\    _/ \_/
/  _/  _/ \_/
\_/  _/ \_/
/ \_/  _/ \_/
\_/ \_/  _/
/ \_/  _/   /
\_/ \_/
  \_/       /
    \_
      \_    /
        \_
          \_/

#7 · Thomas Werner

5 Oct 2012

First modified Hex6 board is isomorphic to SquareHex3, i.e. a modified Hex5 board.

#8 · Thomas Werner

5 Oct 2012

Second modified Hex6 board

_
/ \_
\   \_
/     \_
\    _/ \_
/  _/ \_/ \_
\_/  _/ \_/
/ \_/ \_/ \_/
\_/ \_/ \_/
/ \_/ \_/ \_/
\_/ \_/ \_/
/ \_/ \_/ \_/
\_/ \_/  _/
  \_/ \_/   /
    \_/
      \_    /
        \_
          \_/

#9 · Thomas Werner

5 Oct 2012

not a SquareHex board, diagonals are different from each other

o=====o=====o=====o=====o
I.....I.....I.....I.....I
I..o==o==o==o==o==o==o..o
I..I.....I.....I.....I..I
o==o..o==o==o==o==o..o==o
I..I..I.....I.....I..I..I
I..o==o.....I.....o==o..I
I..I..I.....I.....I..I..I
o==o..o=====o=====o..o==o
I..I..I.....I.....I..I..I
o..o==o.....I.....o==o..o
I..I..I.....I.....I..I..I
o==o..o==o==o==o==o..o==o
I..I.....I.....I.....I..I
I..o==o==o==o==o==o==o..I
I.....I.....I.....I.....I
o=====o=====o=====o=====o

#10 · Thomas Werner

5 Oct 2012

*Previous board should look like this*

o=====o=====o=====o=====o
I.....I.....I.....I.....I
I..o==o==o==o==o==o==o..o
I..I.....I.....I.....I..I
o==o..o==o=o===o==o..o==o
I..I..I....I......I..I..I
I..o==o....I......o==o..I
I..I..o====o......I..I..I
o==o..I.....\.....I..o==o
I..I..I......o====o..I..I
o..o==o......I....o==o..o
I..I..I......I....I..I..I
o==o..o==o===o=o==o..o==o
I..I.....I.....I.....I..I
I..o==o==o==o==o==o==o..I
I.....I.....I.....I.....I
o=====o=====o=====o=====o

#11 · Thomas Werner

5 Oct 2012

The mistakenly posted board two posts above is a further modification of the second modificated Hex6 board. It is obvious that the board

is the same as a SquareHex4 board without a center.

o=====o=====o=====o=====o
I.....I.....I.....I.....I
I..o==o==o==o==o==o==o..o
I..I.....I.....I.....I..I
o==o..o==o==o==o==o..o==o
I..I..I.....I.....I..I..I
I..o==o.....o.....o==o..I
I..I..I..../ \....I..I..I
o==o..o===o o===o..o==o
I..I..I....\ /....I..I..I
o..o==o.....o.....o==o..o
I..I..I.....I.....I..I..I
o==o..o==o==o==o==o..o==o
I..I.....I.....I.....I..I
I..o==o==o==o==o==o==o..I
I.....I.....I.....I.....I
o=====o=====o=====o=====o