Consider a graph $G$ with nonnegative edge weights.

**Question:** In $\mathbb{R}^3$, how hard is it to assign coordinates to vertices such that the Euclidean length of each edge is equal to its weight?

**Question:** Does it get any easier if $G$ is the 1-skeleton of a simplicial surface?

(A similar question was already answered [here][1], but an answer was given only for the special case of complete graphs.)


  [1]: https://mathoverflow.net/questions/33043/algorithm-for-embedding-a-graph-with-metric-constraints