13 Jun
2015
13 Jun
'15
3:38 p.m.
Does Weaire-Phelan refer to the curved-face shape that is the closest known solution to the problem I assume is: ----- Find a lattice on R^3 and a fundamental domain D of unit volume such that its area is minimized over all possible lattices and fundamental domains? ----- Or to the polyhedralization of same? —Dan P.S. Is it known that an absolute minimum exists?
Questions: Exactly what happens to the iso"perimetric" quotient when you delete the interior faces of a Weaire-Phelan unit cell? (For all distinguishable translations.) What is the exact, analytic quotient for Kelvin's cell? (The ISCs don't even recognize 64*π/3/(1 + 2*Sqrt[3])^3.) (Shudder) ditto for the Weaire-Phelan?