Marek has shown me many of the matrixtopes/graphotopes that use 2D intersections to define the shape. Has an extension ever been explored that uses coordinate 3-plane (or 4-plane?) intersections to define shapes, especially when getting into 5D and 6D?
Or, is that method trivial, having no discernible benefit over the current one? If the coordinate 2-planes are second in the number sequence for binomial expansion, then perhaps it is trivial, since 2-planes will always have a lower count than 3, especially in +6D, for example,
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
Unless the coord 3-planes would allow for new shapes not definable with 2-planes....