@article{JTZ-2019,
  author = "Jevti{\'{c}}, Filip D. and Timotijevi{\'{c}}, Marinko and {\v{Z}}ivaljevi{\'{c}}, Rade T.",
   title = "Polytopal Bier Spheres and Kantorovich--Rubinstein Polytopes of Weighted Cycles",
 journal = "Discrete {\&} Computational Geometry",
    year = "2019",
   month = "Nov",
     day = "18",
abstract = "The problem of deciding if a given triangulation of a sphere can be realized as the boundary sphere of a simplicial, convex polytope is known as the `Simplicial Steinitz problem'. It is known by an indirect and non-constructive argument that a vast majority of Bier spheres are non-polytopal. Contrary to that, we demonstrate that the Bier spheres associated to threshold simplicial complexes are all polytopal. Moreover, we show that all Bier spheres are starshaped. We also establish a connection between Bier spheres and Kantorovich--Rubinstein polytopes by showing that the boundary sphere of the KR-polytope associated to a polygonal linkage (weighted cycle) is isomorphic to the Bier sphere of the associated simplicial complex of ``short sets''.",
    issn = "1432-0444",
     doi = "10.1007/s00454-019-00151-5",
     url = "https://doi.org/10.1007/s00454-019-00151-5"
     archivePrefix = "arXiv",
            eprint = {1812.00397},
}