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This item is a game information page
It belongs to categories: Orthodox chess, 
It was last modified on: 2002-11-01
 By Mark  Thompson. Tetrahedral Chess. Three dimensional variant with board in form of tetrahedron. (x7, Cells: 84) [All Comments] [Add Comment or Rating]
Mark Thompson wrote on 2004-01-24 UTC
Charles, after reading your latest about the rhombic dodecahedral grid, I thought to look up 'rhombic dodecahedron' in the invaluable Penguin Dictionary of Curious and Interesting Geometry, where I found the following tidbits you might find interesting: 'rhombic dodecahedron: Take a three-dimensional cross formed by placing six cubes on the faces of a seventh. Join the centres of the outer cubes to the vertices of the central cube. The result is a rhombic dodecahedron. ... From the original method of construction, it follows that rhombic dodecahedra are space-filling.' [etc.] Indeed, if you imagine space filled with alternating black and white cubes, and perform the construction by dividing up the white cubes into six pyramids apiece and affixing them onto their black cube neighbors, you get the r. d. grid, and this supports your observation that the grid is conceptually identical to the cubic grid with the white cubes removed.