Ecila

Ecila ("Alice" backwards) is a 6-dimensional game that appears in V.R. Parton's pamphlet Chessical Cubism. It appears immediately after, and is a higher dimensional analogue of, Sphinx Chess. It appears to have been invented over a decade before publication in the pamphlet however, appearing in the 9 September 1957 The Birmingham Post, according to John Beasley's Toward ECV3

Setup

The game is set on a 2x2x2 array of 2x2x2 cubes. (Parton also suggests a 2x2x2 array of 3x3x3 cubes.) Parton does not give a starting array (or even piece set), instead suggesting an initial setup phase during which the players alternate turns placing pieces that have been decided on prior to play.

Pieces

As in Sphinx Chess, the basic pieces move either within their cube or between cubes, but not both in the same move.  These are the Rook, Bishop, and Unicorn, which move orthogonally, diagonally, and triagonally (respectively) either (1) within the current cube or (2) to a new cube, treating the 2x2x2 array as a 3D board itself (and ending at the square with the same relative position in the new cube as their current position).  The Rook and Bishop both attack six cells from any position, while the Unicorn attacks only two.  The Rook can reach any square eventually, while the Bishop induces four bindings (which Parton uses to color the board), and each Unicorn can only reach four positions (one of each color).

Parton gives two possible Queen definitions, R+B or R+B+U.  He also introduces a Narwhal, which is R+U.

Unlike in Sphinx Chess, Parton does provide other pieces that in their moves may (and in fact must) move to a different position of a different cube.  They are the Horse, Hippogriff, and Wyvern.  The Horse moves between cubes as a Rook followed by a Bishop move in the new cube (ignoring the intermediate cell, and so makes a triagonal move different from the Unicorn).  The Hippogriff moves between cubes as a Rook followed by a Unicorn move in the new cube (so makes a particular kind of 4-dimensional step).  The Wyvern moves as a Bishop between cubes followed by a Unicorn step in the new cube (so a particular kind of 5-dimensional step).  The Horse attacks 9 cells, while the Hippogriff and Wyvern only 3.  The Horse is restricted to half the board, two of the Bishop bindings put together.  Parton doesn't say, but it seems that the Hippogriff and Wyvern each can reach one eighth of the board (but different eighths).

Parton also leaves unsaid the obviously (or is that just me?) omitted movements like bishop-between-cubes+rook-within-cube.

Finally, the King is given several possible definitions (as is often the case in higher dimensions, checkmate may be difficult, so several limitations are suggested): R+B(=Q, maybe), or just R, or maybe even just B.  Or maybe restricted to one cube.

Notes

Parton also mentions the Losing Chess version of the game, and a kingless game in which the goal is elimination of all the opponent's pieces.

Ecila was revisited in Issue 54 of the Variant Chess magazine (by John Beasley?); the board is identified to an ordinary chessboard (2x2x2x2x2x2=64) with different coloring of the squares, and the king is assumed to move as R. With some additional tweaks (kings can double-step from their home square, stalemate is a win), K+Q and K+P vs lone K are shown to be wins (the latter when the pawn is protected). In working toward a starting position, Queens are decided to be too powerful, and versions of the higher-dimensional steppers are also discarded, favoring just King, Pawn, Rook, Bishop, and maybe Unicorn.

Last revised by Ben Reiniger.