Non-Euclidean Chess Board (Wormhole)

This “Wormhole Chess Board” is composed of two back-to-back regular sized chess boards connected by a catenoid surface through the central 4 x 4 grid of squares on each board.

Actual game play on this board is beyond challenging so unless you’re a genius, this board is more of an art or conversation piece.

Part of what makes game play so challenging is the presence of the eight pentagons that are required to transition between the flat and curved surfaces.

Here are a few suggestions if you want to try playing.

Moving a piece through a pentagon allows for additional movement options. When entering from a column or row on the flat surface (such as with a rook) there are two exit options, one that allows the piece to remain on the flat surface and another that allows the piece to enter the wormhole. The reverse is true when entering a pentagon from the wormhole. When entering a pentagon from a diagonal (such as with a bishop) there are two options for exiting the pentagon, both of which allow the piece to remain on its own colour.

The model above shows two separate sets of pieces for each player, facing each other across the flat surface as well as through the curved surface. This means that there are two kings, which complicates the end game somewhat!

Another option would be to play as a four-player game with each set of pieces a different colour.

If anyone comes up with a comprehensive set of rules for incorporating the pentagons into game play, please share them!

Here are printing and assembly instructions:

For the board, print two of each of the “Flat Board Half” and “Wormhole Half” files. No supports needed. Glue together carefully.

For the square, you will need a total of 4 “Quadrant of Squares” for each colour. Note that there are small reference dimples on the bottom of the curved pieces. When properly positioned, the dimples will point towards the pentagonal piece.

Playing pieces are remixed from “Mini Chess for Altoid Box” by “humphrey_b52.” Holes have been added for 1/8” by 1/8” cylindrical magnets. Note that these pieces are scaled smaller than those sets provided for my other “Spherical” and “Hyperbolic Paraboloid” chess boards. The small size is necessary so that the pieces don’t collide when passing side-by-side through the wormhole.