4
$\begingroup$

Given a fixed volume and fixed surface area I would like to construct polyhedra that minimize the total length of the edges. This seems like a straight-forward problem to solve by brute force for reasonably small number of vertices, but I imagine this has already been done, or at least considered.

Can anybody think of a source for such structures?

Improve this question
$\endgroup$
1

1 Answer 1

Reset to default
3
$\begingroup$

This has been considered, see, for example, this report.

Improve this answer
$\endgroup$
2
  • 2
    $\begingroup$ From Igor's link: [B01] S. Berger, Edge Length Minimizing Polyhedra, Thesis, Rice University, (2001) $\endgroup$
    – Joseph O'Rourke
    Commented Dec 7, 2013 at 21:54
  • $\begingroup$ Thanks for the citation, but the thesis looks at either fixed area or fixed volume. A more concrete example of the question would be: find a shape that encloses 1m^3 of volume, using 5m^2 of flat material, s.t. the total length of the seams is minimized. $\endgroup$
    – Rodrigo
    Commented Dec 8, 2013 at 10:47

You must log in to answer this question.

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