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  "title": "A mosaic beyond the proposed band",
  "shortTitle": "Rational Laguerre mosaics",
  "url": "https://evidencepress.org/releases/rational-laguerre-mosaics/",
  "oneLine": "An exact periodic arrangement of convex cells has harmonic degree 468/115—strictly above the proposed three-dimensional ceiling of four.",
  "abstract": "A rational normal face-to-face convex mosaic has densities (V,C,I)=(373,432,3276) and harmonic degree 468/115. Exact periodic weighted-Delaunay and Laguerre realizations accompany the finite certificate. Written extensions attain every harmonic degree in (3,16) and identify the finite closure in the periodic regular class with asymptotic four-polytope vertex–facet complexity. Neither a maximum of 16 nor a classification of all mosaics is established.",
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    "name": "Harmonic-degree band for normal convex face-to-face mosaics",
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    {
      "citation": "Domokos and Lángi, On some average properties of convex mosaics. Target band and normality assumptions.",
      "url": "https://doi.org/10.1080/10586458.2019.1691090",
      "doi": "10.1080/10586458.2019.1691090"
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      "citation": "Joswig and Ziegler, Neighborly cubical polytopes. Inherited polytope construction.",
      "url": "https://doi.org/10.1007/s004540010039",
      "doi": "10.1007/s004540010039"
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      "url": "https://arxiv.org/abs/math/0208073",
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    {
      "citation": "Ziegler, Projected products of polygons. Family approaching complexity 16.",
      "url": "https://doi.org/10.1090/S1079-6762-04-00137-4",
      "doi": "10.1090/S1079-6762-04-00137-4"
    },
    {
      "citation": "Rybnikov, Stresses and liftings of cell-complexes. Lifting background.",
      "url": "https://doi.org/10.1007/PL00009434",
      "doi": "10.1007/PL00009434"
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