Re: [math-fun] A use for Jud's method

I'm getting very intrigued to know what number Jud's method would produce in the 4-dimensional case. The point there is not that the method MIGHT not produce a 25-sphere example that MIGHT exist (but almost certainly DOESN'T), but that it WON'T produce the 24-sphere example that definitely DOES exist (and is almost certainly UNIQUE). This is because that configuration has the shape of the regular polytope {3,4,3}, from which you can see that its cells are octahedra rather than the tetrahedra that Jud's method requires. Maybe the method won't even find so many as 20 spheres? John Conway