George Duke wrote on Wed, Jul 2, 2008 04:30 PM UTC:
[Maybe Paulowich could explain again how to read Comments 26+ in threads, which is readily done in articles.] Mark Thompson's Tetrahedral Chess is on our recognized list at Chessboard Math. Here's a variant 3-D board also with 84 squares, now called Pyramid (another different 3d has name Pyramidal already). One block, or cell, sits centrally atop 3x3 cells, then 3x3 above 5x5, then 7x7. Four levels, or layers, each of 1, 9, 25, 49 cells respectively (=84). Connectivity is easier to visualize than Tetrahedral, and there are all the usual orthogonal, diagonal and triagonal directions of Raumschach
(125 cubes, 1907). At the one-cell top level, a Rook has only one
direction to move through, first 3x3, then 5x5, and in three steps to the
very center of the bottom 7x7. Raumschach King at any corner has 7 cells to which to move, whereas Pyramid King, also omnidirectional, would have only four from the lower corners.
