Pith. sign in

REVIEW 3 cited by

Classification of Reflexive Polyhedra in Three Dimensions

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv hep-th/9805190 v1 pith:KWWDMY3C submitted 1998-05-27 hep-th math.AG

M. Kreuzer , H. Skarke This is my paper · ORCID
classification hep-thmath.AG
keywords polyhedrareflexivealgorithmclassificationconnecteddimensionsthreeapplication
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We present the last missing details of our algorithm for the classification of reflexive polyhedra in arbitrary dimensions. We also present the results of an application of this algorithm to the case of three dimensional reflexive polyhedra. We get 4319 such polyhedra that give rise to K3 surfaces embedded in toric varieties. 16 of these contain all others as subpolyhedra. The 4319 polyhedra form a single connected web if we define two polyhedra to be connected if one of them contains the other.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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

  1. Constraining F-theory Model Building with QCD Axions

    hep-th 2026-05 unverdicted novelty 5.0 of 10

    QCD axions constrain F-theory base threefolds to have rigid or flux-rigidified divisors, yielding typical axion masses around 10^{-9} eV and decay constants near 10^{15} GeV in allowed regions.

  2. Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds

    hep-th 2025-02 conditional novelty 5.0 of 10

    Mass deformations of 2d (0,2) brane brick models are shown in four explicit examples to implement birational transformations of toric Calabi-Yau 4-folds, including non-reflexive toric diagrams.

  3. Beyond Algebraic Superstring Compactification

    hep-th 2025-02 conditional novelty 5.0 of 10

    Calabi-Yau compactifications and mirror symmetry are conjecturally extended to non-algebraic toric spaces using Laurent deformations and the 'intrinsic limit' completion.

Pith tools