Minimizing the mass of the codimension two skeleton of convex, unit volume polyhedra Ryan Scott 52B6049Q1528A75edge-minimizingpolytopesfunctions of bounded variationcurrents In this paper we establish the existence and partial regularity of a $(d-2)$-dimensional edge length minimizing polyhedron in $\mathbb{R}^d$. The minimizer is a generalized convex polytope of volume $1$ which is the limit of a minimizing sequence of polytopes converging in the Hausdorff metric. We show that the $(d-2)$-dimensional edge length is lower-semicontinuous under this sequential convergence. Here the edge set of the limit generalized polytope is a closed subset of the boundary whose complement in the boundary consists of countably many relatively open planar regions. The case $d=3$ was previously obtained by S. Berger [S. Berger, \textit{Edge length minimizing polyhedra}, Ph.D. thesis (2002), Rice University]. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4734 10.1512/iumj.2012.61.4734 en Indiana Univ. Math. J. 61 (2012) 1513 - 1564 state-of-the-art mathematics http://iumj.org/access/