Thursday, February 22, 2018

[mkhbjbvh] Chess on a hypercube

Adapt chess on the surface of a 6x6x6 cube to the hypersurface (a 3D manifold) of a 6x6x6x6 4D hypercube (tesseract).  Apply this movement of 3D chess pieces.

A tesseract has 8 cubical cells that comprise its hypersurface.  There are the top and bottom cubes (promotion areas), and 6 side cubes which are connected roughly as the 6 faces of a cube are, as seen in the famous cube-within-a-cube cell-first perspective projection of the tesseract.

There are some literal edge cases of bishops hitting edges that need to be thought through (probably movement through an edge prohibited), similar to bishops hitting corners when playing on the surface of a cube.  3D knight moves through edges and rooks through corners also require thought.

Each player starts with 216 pawns, 54 rooks, 54 bishops, 54 knights, 27 queens, 26 commoners, and 1 king: total 432.  Board area 1728.

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