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Henry
Posts:
1,089
Registered:
12/6/04


Re: Menger's theorem question
Posted:
Jan 20, 2011 11:58 AM


On Jan 17, 6:28 pm, Robert Israel <isr...@math.MyUniversitysInitials.ca> wrote:
> Surely it depends on the polyhedron? E.g. for an octahedron there > are 4 pairwise vertexindependent paths between nonadjacent > vertices.
4 paths for adjacent vertices too.
Indeed the number of pairwise vertexindependent paths for any pair of nonidentical vertices from any Platonic polyhedron is equal to the number of edges meeting at each vertex (so 3 for a tetrahedron, cube or dodecahedron, 4 for an octahedron and 5 for an icosahedron).



