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All Weight Systems for Calabi-Yau Fourfolds from Reflexive Polyhedra

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arxiv 1808.02422 v1 pith:XUVC3VKS submitted 2018-08-07 hep-th math.AG

Friedrich Schöller , Harald Skarke This is my paper · ORCID
classification hep-thmath.AG
keywords reflexivepolytopesweightscalabi-yaufourfoldspolyhedrasystemstuples
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abstract

For any given dimension $d$, all reflexive $d$-polytopes can be found (in principle) as subpolytopes of a number of maximal polyhedra that are defined in terms of $(d+1)$-tuples of integers (weights), or combinations of $k$-tuples of weights with $k<d+1$. We present the results of a complete classification of sextuples of weights pertaining to the construction of all reflexive polytopes in five dimensions. We find 322 383 760 930 such weight systems. 185 269 499 015 of them give rise directly to reflexive polytopes and thereby to mirror pairs of Calabi-Yau fourfolds. These lead to 532 600 483 distinct sets of Hodge numbers.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Calabi-Yau Threefolds from Vex Triangulations

    hep-th 2025-12 conditional novelty 7.0 of 10

    All fine regular triangulations of 4D reflexive polytopes—including non-FRST vex triangulations—yield smooth, birationally equivalent Calabi-Yau threefold hypersurfaces.

  2. What to do with a Ricci-flat Calabi--Yau metric?

    hep-th 2026-05 unverdicted novelty 3.0 of 10

    Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.

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