0
$\begingroup$

A. Up to isomorphism, how many polyhedra with N faces are there? Assume each face can be a triangle, square, pentagon, hexagon, etc... Furthermore each edge can be resized to any nonzero positive length to obtain an isomorphic polyhedron. (to be clear, all the faces get assembled together into a 3D, multifaced diamond-like object so as to speak).

B. As a related question, up to isomorphism, how many polyhedra with M edges exist?

NOTE: There are only 5 platonic solids, but in my question the faces can be any shape with straight edge perimeter and the faces don't have to be regular).

C. Does the answer to these questions change if the faces must be regular (same size edges for each face)?

Improve this question
$\endgroup$
3
  • $\begingroup$ You need to tell us exactly what you mean by isomorphism. $\endgroup$
    – Mariano Suárez-Álvarez
    Commented Jun 9, 2016 at 21:38
  • 4
    $\begingroup$ I think that by duality this is the same as the number of polyhedra with $N$ vertices. That's tabulated at oeis.org/A000944 where there is also a link to numericana.com/data/polyhedra.htm $\endgroup$
    – Gerry Myerson
    Commented Jun 9, 2016 at 23:04
  • $\begingroup$ Would it be hard to come up with an algorithm to solve this problem? $\endgroup$
    – Jack Maddington
    Commented Jul 10, 2016 at 23:15

0

Reset to default

You must log in to answer this question.