“
The Cube Space” is a name given to
the eightfold cube in a vulgarized mathematics text,
Discrete Mathematics: Elementary and Beyond, by
Laszlo Lovasz et al., published by Springer in 2003. The identification in a natural way of the eight points of the linear 3-space over the 2-element field GF(2) with the eight vertices of a cube is an elementary and rather obvious construction, doubtless found in a number of discussions of discrete mathematics. But the less-obvious generation of
the affine group AGL(3,2) of order 1344 by permutations of parallel edges in such a cube may (or may not) have originated with me. For descriptions of this process I wrote in 1984, see
Diamonds and Whirls and Binary Coordinate Systems. For a vulgarized description of this process by Lovasz, without any acknowledgement of his sources, see an excerpt from his book.
