We describe our package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet. It contains routines for vertex and facet enumeration, computation of incidences and symmetries, as well as completion of the set of lattice points in the convex hull of a given set of points. In addition, there are procedures specialised to reflexive polytopes such as the enumeration of reflexive subpolytopes, and applications to toric geometry and string theory, like the computation of Hodge data and fibration structures for toric Calabi-Yau varieties. The package is well tested and optimised in speed as it was used for time consuming tasks such as the classification of reflexive polyhedra in 4 dimensions and the creation and manipulation of very large lists of 5-dimensional polyhedra. While originally intended for low-dimensional applications, the algorithms work in any dimension and our key routine for vertex and facet enumeration compares well with existing packages. (Source:

References in zbMATH (referenced in 37 articles , 1 standard article )

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  1. He, Yang-Hui; Jejjala, Vishnu; Pontiggia, Luca: Patterns in Calabi-Yau distributions (2017)
  2. Anderson, Lara B.; Apruzzi, Fabio; Gao, Xin; Gray, James; Lee, Seung-Joo: A new construction of Calabi-Yau manifolds: generalized CICYs (2016)
  3. Berman, Robert J.: K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics (2016)
  4. Karzhemanov, Ilya: Fano threefolds with canonical Gorenstein singularities and big degree (2015)
  5. Cicoli, Michele; Klevers, Denis; Krippendorf, Sven; Mayrhofer, Christoph; Quevedo, Fernando; Valandro, Roberto: Explicit de Sitter flux vacua for global string models with chiral matter (2014)
  6. Long, Cody; Mcallister, Liam; Mcguirk, Paul: Heavy tails in Calabi-Yau moduli spaces (2014)
  7. Berman, Robert J.; Berndtsson, Bo: Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties (2013)
  8. Braun, Volker: Toric elliptic fibrations and F-theory compactifications (2013)
  9. Gao, Xin; Shukla, Pramod: On classifying the divisor involutions in Calabi-Yau threefolds (2013)
  10. Lüst, Dieter; Zhang, Xu: Four Kähler moduli stabilisation in type IIB orientifolds with $K3$-fibred Calabi-Yau threefold compactification (2013)
  11. Cicoli, Michele; Kreuzer, Maximilian; Mayrhofer, Christoph: Toric $K3$-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications (2012)
  12. Cicoli, Michele; Mayrhofer, Christoph; Valandro, Roberto: Moduli stabilisation for chiral global models (2012)
  13. Blumenhagen, Ralph; Jurke, Benjamin; Rahn, Thorsten: Computational tools for cohomology of toric varieties (2011)
  14. Blumenhagen, Ralph; Rahn, Thorsten: Landscape study of target space duality of (0, 2) heterotic string models (2011)
  15. Braun, Volker: On free quotients of complete intersection Calabi-Yau manifolds (2011)
  16. Christophersen, Jan Arthur: Deformations of equivelar Stanley-Reisner abelian surfaces (2011)
  17. Clancy, Robert: New examples of compact manifolds with holonomy Spin(7) (2011)
  18. Davies, Rhys: Hyperconifold transitions, mirror symmetry, and string theory (2011)
  19. He, Yang-Hui; Kreuzer, Maximilian; Lee, Seung-Joo; Lukas, Andre: Heterotic bundles on Calabi-Yau manifolds with small Picard number (2011)
  20. Knapp, Johanna; Kreuzer, Maximilian: Toric methods in F-theory model building (2011)

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