Discussing higher dimensions, it says: “For n>1, a lower bound of n+2 is available using a generalization of the Moser spindle: a pair of the objects (each 2 simplexes glued together on a facet) which are joined on 1 side by a point and the other side by a line.”

The line at the other end of the spindle can instead be a simplex of n-1, which gives a lower bound of 2n.

]]>It’s difficult to imagine what a valid chromatic coloring of the plane might look like if CNP is 5 or 6, since it couldn’t be symmetrical in the same way as this pattern. Maybe something semiperiodic based on Penrose Tiles? Perhaps someday someone will discover it and it will take over the world like the Mandelbrot Set did. ðŸ™‚ (Admittedly it might be unvisualizeable like the Banach-Tarski division.)

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