Let G be the group of 1344 transformations of the
3-dimensional affine finite geometry over the 2-element field
GF(2).
The
eightfold cube illustrates one property of physical space--
namely, the invariance under G of the set of seven
partitions
illustrated with kindergarten blocks below.
These seven
partitions are a model, in physical space, of the seven points
of
the 2-dimensional projective finite geometry over GF(2). The partitions
(i.e., the projective points) are permuted by G, a group generated by
physically natural permutations of the eight subcubes.
