Today's earlier post mentions one approach to the concepts of unity and multiplicity. Here is another.

http://www.log24.com/log/pix11A/110427-Cube27.jpg
Unity:
The 3×3×3 Galois Cube

Ed Pegg Jr.'s program at Wolfram demonstrating concepts of a 1985 note by Cullinane

Multiplicity:

One of a group, GL(3,3), of 11,232
natural transformations of the 3×3×3 Cube

See also the earlier 1985 3×3 version by Cullinane.