Normal surface weight
= Normal surface weight
{title2=$w(F)=|F\cap T^{(1)}|$}
The weight of a <normal surface> counts its intersections with the edges of the <triangulation>. It is a positive linear function of its coordinates: each corner of a normal <disk> contributes the reciprocal of the number of tetrahedral sectors around its edge. Thus a nontrivial decomposition into compatible coordinate vectors gives both summands strictly smaller weight.