EDITOR’S NOTE: Since I have written this I have come to recognize limitations in this and related perspectives that led them to be cul-de-sacs. My more recent work can be found here: The Czerepak Framework
After considerable struggle with the data it became clear to me that I was not dealing with a table in the normal sense. I could not reconcile a data cube with the seven dimensions I had discovered. Then it occurred to me that I was not dealing with a cube at all. I was dealing with a simpler solid, the octahedron. The octahedron has six dimensions (spokes) and seven vertexes.
This gives us a Hauy Construction (this figure is an eight degree):
Using my new taxonomy gives us the following views:
The age of the cube is over. Welcome to the age of the Octahedral Hauy Construction.