The space of planes in R^3 is also 3-dimensional, so this problem could be visualised by a three-dimensional diagram, with each point "colored" with the number of sides of the intersection of the corresponding plane with a reference dodecahedron. This diagram has dodecahedral symmetry, and a finite number of regions. Complete analysis is only a matter of elbow grease. On Sun, Aug 4, 2019 at 9:28 PM James Propp <jamespropp@gmail.com> wrote:

It appears that no cross-section of a regular dodecahedron has more than ten sides, but how does one prove it? (I did five minutes of Googling but didn't find relevant literature.)

Thanks,

Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun