@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}, }