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Tetrahedral Chess. Three dimensional variant with board in form of tetrahedron. (7x(), Cells: 84) [All Comments] [Add Comment or Rating]

💡📝Mark Thompson wrote on Sat, Jan 24, 2004 10:30 PM 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.