Finite
Geometry Notes |

"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 the following excerpt
from his book.

Page created October 24, 2008, by Steven H. Cullinane

Page created October 24, 2008, by Steven H. Cullinane