Log24

“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”

— Hermann Weyl, Philosophy of  Mathematics and
    Natural Science , Princeton, 1949, p. 237

Melissa C. Wong, illustration for "Atlas to the Text,"
by Nicholas T. Rinehart:

The above fanciful illustration pictures 6_*9=54 colored squares on the six 
faces of a 3x3x3 cube.

Compare and contrast the Aitchison  labeling, not unlike the one above,
of 6*4=24 unit squares (or, equivalently, 24 pips  at the squares' centers)
on a 2x2x2 cube.

Now consider how the 8-square "brick" of R. T. Curtis may be colored with
four colors using the 105 ways to partition its eight squares into four 2-sets.

By analogy, the 24  squares on a cube's  surface, as above, afford a cubical
space for applying six  colors to the sextet  partitions (into six 4-sets) of Curtis's
Miracle Octad Generator (MOG), using Aitchson's cubical model (with, of course,
the parts to be moved being pips or squares rather than cuboctahedron edges). 

The 4-coloring of Curtis bricks is useful in picturing the Klein correspondence.
Are there similar uses of  cube  6-colorings? Or 4-colorings? (Group actions on
a 6-set are of considerable combinatorial and algebraic interest because of
the exceptional outer automorphism of S₆.)

For a colored presentation of sextet space modeled with a rectangle,
as in the Curtis MOG, see . . .

https://xenon.stanford.edu/~hwatheod/mog/mog.html .