Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: polyhedra/graph question
Replies: 2   Last Post: Jan 27, 1999 2:38 PM

 Messages: [ Previous | Next ]
 Helena Verrill Posts: 8 Registered: 12/6/04
polyhedra/graph question
Posted: Jan 27, 1999 2:03 PM

Ages ago, some one asked on this list (I think)
for a description of all possible planar graphs with all
vertices degree 3, and all faces having 5 or 6

Did anyone get round to finding the solution yet?
there are about 4 pairs (n,a,b) such that there are
infinitely many graphs with n the degree of each
vertex, and a, b the possible numbers of sides of a face.
for each possible set (n,a,b), I can find loads of infinite
families, but I've no idea how to get everything.

Here's a nice little thing: if you have degree 4
vertices, and faces are either squares or triangles,
show that you have to have an even number of vertices.

I'd like to know - is this a topological property,
or something else? (Cos I didn't prove with with
Euler, but it would be nice to know if there was a
'topological' way to prove it, and if it has generalizations, etc)

Helena

Date Subject Author
1/27/99 Helena Verrill
1/27/99 John Conway
1/27/99 Helena Verrill