Re: [math-fun] Random slice of a cube

On Sun, Oct 15, 2017 at 3:22 PM, Keith F. Lynch <kfl@keithlynch.net> wrote:

I'm pretty sure it's not possible to get a polygon with fewer than four sides from a plane's intersection with an octahedron, or with fewer than five sides from a plane's intersection with an icosahedron.

With an octahedron, you can get an intersection in a point, a line, one of the faces (three sides), or a deeper cross section with four or more sides. With an icosahedron, you can get an intersection in a point, a line, one of the faces (three sides, a plane that intersects the base of a face but goes just below one of the other vertices (four sides) or more. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com