Toric Calabi-Yau Database

This database is based on: arXiv:1411.1418, arXiv:1706.09070, and most recently arXiv:2111.03078. Please cite us!
Contact Ross Altman with questions.
Constructed with support from the National Science Foundation under grant NSF/CCF-1048082, EAGER: CiC: A String Cartography.
  1. Basic Query
  2. Advanced Query

    Enter search parameters:

    Format: Integers


  • Polytope ID #:

    • Format: Integers


  • h11:
  • h21:
  • Euler #:
  • Favorable?:
  • Fundamental Group:

    • Format: Integers


  • Polytope #:
  • Geometry # (within polytope):
  • Triangulation # (within geometry):
  • Triangulation # (within polytope):

    • Format: Integers


  • # of Geometries (within polytope):
  • # of Triangulations (within geometry):
  • # of Triangulations (within polytope):

    • Format: Integers


  • # of Newton Polytope Vertices:
  • # of Newton Polytope Points:
  • # of Dual Polytope Vertices:
  • # of Dual Polytope Points:

    • Format: {{...},{...},...,{...}}

    (Mathematica matrix)


  • (Resolved) Weight Matrix:
  • Newton Polytope Vertex Matrix:
  • Dual Polytope (Resolved) Vertex Matrix:
  • CY 2nd Chern Numbers:
  • Intersection Polynomial or Tensor:

    Select Polytope Properties:

  • Polytope ID #
  • Polytope #
  • H11
  • H21
  • Euler #
  • Favorable?
  • # of Newton Polytope Vertices
  • # of Newton Polytope Points
  • Newton Polytope Vertex Matrix
  • # of Dual Polytope Vertices
  • # of Dual Polytope Points
  • Dual Polytope Vertex Matrix
  • Dual Polytope Resolved Vertex Matrix
  • Weight Matrix
  • Resolved Weight Matrix
  • Toric to Basis Divisor Transformation Matrix
  • Basis from Toric Divisors
  • Basis to Toric Divisor Transformation Matrix
  • Toric from Basis Divisors
  • Fundamental Group
  • # of Geometries (within polytope)
  • # of Triangulations (within polytope)

    Select CY Geometry Properties:

  • Geometry # (within polytope)
  • # of Triangulations (within geometry)
  • CY 2nd Chern Class (Basis)
  • CY 2nd Chern Numbers
  • CY Intersection Polynomial (Basis)
  • CY Intersection Tensor (Basis)
  • CY Mori Cone Matrix
  • CY Kahler Cone Matrix
  • Toric Swiss Cheese Solutions
  • Explicit Swiss Cheese Solutions

    Select Triangulation-Specific Properties:

  • Triangulation # (within geometry)
  • Triangulation # (within polytope)
  • Triangulation
  • Stanley-Reisner Ideal
  • Ambient Chern Classes (Toric)
  • Ambient Chern Classes (Basis)
  • CY 2nd Chern Class (Toric)
  • CY 3rd Chern Class (Toric)
  • CY 3rd Chern Class (Basis)
  • Ambient Intersection Polynomial (Toric)
  • Ambient Intersection Tensor (Toric)
  • Ambient Intersection Polynomial (Basis)
  • Ambient Intersection Tensor (Basis)
  • CY Intersection Polynomial (Toric)
  • CY Intersection Tensor (Toric)
  • Phase Mori Cone Matrix
  • Phase Kahler Cone Matrix

Count Only:

Match:   

(0 = Unconstrained)