By a theorem of Minkowski from 1903, an $n$-dimensional polytope $P\subset \mathbb R^n$ is determined up to translation by its unit face normal $u_1,\dots,u_k\in S^{n-1}$ and the corresponding $(n-1)$ dimensional facet areas $a_1,\dots,a_k>0$ that satisfy $\sum_i a_i u_i = 0$.
I am looking for algorithms that actually implement this reconstruction, mainly in 3 dimensions.
This has been discussed in this MO question, where a reference to an article of Gritzmann and Hufnagel on the algorithmic complexity of the problem is given. I also found the recent preprint of Sellaroli, that describes how to reduce the problem in 3 dimensions to a root finding problem of a vector function. It refers to an implementation in a GitHub repository that unfortunately only contains a license text.
Is any actual implementation of an algorithm for Minkowski reconstruction in 3 dimensions available?
