3
$\begingroup$

How many unique vertex transitive polyhedra exist where each vertex has 3 incident edges for polyhedra with n (= # faces) > 3 ?

Improve this question
$\endgroup$

2 Answers 2

Reset to default
3
$\begingroup$

The complete list of vertex transitive planar graphs was determined in 1979 by Fleischner and Imrich. See here. To quote:

Theorem 3. The connected, simple, planar vertex-transitive graphs are the single vertex, the single edge, simple circuits and the nets of the uniform convex polyhedra, namely the nets of regular prisms and antiprisms, the Platonic and the Archimedian bodies.

Improve this answer
$\endgroup$
0
$\begingroup$

See

MR0130841 (24 #A695) Reviewed Tutte, W. T. A census of planar triangulations. Canad. J. Math. 14 1962 21–38. 05.65 (52.45)

Improve this answer
$\endgroup$
2
  • 1
    $\begingroup$ You missed "vertex transitive" in the question, I believe. $\endgroup$
    – Brendan McKay
    Commented Apr 28, 2014 at 2:54
  • $\begingroup$ @BrendanMcKay Yes, I did :( $\endgroup$
    – Igor Rivin
    Commented Apr 28, 2014 at 3:00

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .