I have made this Hexagonal Chess for three players...

The inventor of the chessboard was Matt Seaburry...

(In the First Line he had only 4 pawns)

 

The Knight moves:

one Hexagon like the Rook and then one Hexagon like the Bishop...

or

one Hexagon like the Bishop and then one Hexagon like the Rook...

 

The pawns move in two directions:

or forward-right or forward-left...

 

That is a fun way to play chess.  I don't play much chess anymore, but when I was in High School (1964) my friends and I played hexagonal chess on a board very similar to what you show.  I don't remember all the rules, and don't know who invented it-- but it was fun and challenging.

Look at the webside:

http://www.chessvariants.com/multiplayer.dir/treyshah.html

He plays wrong the Knight and the pawns!!!...

But his Hexagon Chessboard is great!!!...

I made it after 20 years when I First saw it in a magazine...

Now I cannot find again the NERO RED chesspieces...