Query the Toric Calabi-Yau Database
About ToricCY Database

This database is based on arXiv:1411.1418, arXiv:1706.09070, and arXiv:2111.03078. Please cite us!

Constructed with support from the National Science Foundation under grant NSF/CCF-1048082, EAGER: CiC: A String Cartography.

Contact Ross Altman with questions.

Need the full dataset? Download the packaged ToricCY database for local analysis.
This interface lets you build safe structured queries against the ToricCY dataset. Use the controls below to select joins, projections, and result granularity — then run queries to preview or export results.
Polytope Features (POLY)
Cursor-paged POLY, used as the root for joins.
Sort
Page size
POLY columns (output)
Optional. You can return zero Polytope columns and only join-level columns.
POLYID is always used internally for joins/paging but is not returned unless you select it.
Identifiers & join keys
Matched row counts
Topological invariants
Polytope vertex features
Combined weight systems
Basis transformations
Polytope WHERE conditions
Add zero or more conditions. For in, use comma-separated values.
No conditions.
Polytope-derived Features
Required joins are locked based on result level. Each join is limited per parent inside its lookup pipeline.
Join sort field
Dir
Per-parent cap
GEOM fields (flattened columns)
Identifiers & join keys
Matched row counts
Topological invariants
Mori & Kähler cone matrices
GEOM WHERE conditions
Add zero or more conditions. For in, use comma-separated values.
No conditions.
Join sort field
Dir
Per-parent cap
TRIANG fields (flattened columns)
Identifiers & join keys
Matched row counts
Topological invariants
Triangulation decompositions
Algebraic features
Mori & Kähler cone matrices
TRIANG WHERE conditions
Add zero or more conditions. For in, use comma-separated values.
No conditions.
Join sort field
Dir
Per-parent cap
INVOL fields (flattened columns)
Identifiers & join keys
Matched key counts
Topological invariants
Manifold smoothness features
Orientifold involution features
INVOL WHERE conditions
Add zero or more conditions. For in, use comma-separated values.
No conditions.
Join sort field
Dir
Per-parent cap
SWISSCHEESE fields (flattened columns)
Identifiers & join keys
Topological invariants
Swiss-cheese LVS structures
SWISSCHEESE WHERE conditions
Add zero or more conditions. For in, use comma-separated values.
No conditions.
Run query
Result level controls the deepest stage to unwind/page to.
Result level
Auto: POLY
Results
#
No results.
Tip: drag headers to reorder · click header to sort · drag header edge to resize · click a cell to copy · click row # to copy row · click header “Copy” to copy column.
TSV export sanitizes tabs/newlines inside cells to keep the output rectangular.
Note: paging controls move through POLY pages. Join caps limit fan-out per parent inside lookups.