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# barycentricSubdivision -- the barycentric subdivision of a simplicial complex.

- Usage:
    `barycentricSubdivision D`
    `barycentricSubdivision F`
- Inputs:
  - D, an abstract simplicial complex,
  - F, a list, a list of facets defining a simplicial complex
- Outputs:
  - an abstract simplicial complex, the barycentric subdivision of a simplicial complex of D

## Description

The following example uses the simplicial complex on four vertices composed of two disconnected edges.

    i1 : S = QQ[a,b,c,d];

    i2 : F = {a*b,c*d};

    i3 : D = simplicialComplex F

    o3 = simplicialComplex | cd ab |

    o3 : SimplicialComplex

    i4 : barycentricSubdivision D

    o4 = simplicialComplex | v_0v_4v_6 v_0v_3v_6 v_0v_2v_5 v_0v_1v_5 |

    o4 : SimplicialComplex

    i5 : barycentricSubdivision F

    o5 = simplicialComplex | v_0v_4v_6 v_0v_3v_6 v_0v_2v_5 v_0v_1v_5 |

    o5 : SimplicialComplex

## See also

- SimplicialComplexes -- exploring abstract simplicial complexes within commutative algebra
- Posets -- a package for working with partially ordered sets
- SimplicialDecomposability -- various decomposability routines for simplicial complexes.

## Ways to use barycentricSubdivision:

- `barycentricSubdivision(List)`
- `barycentricSubdivision(SimplicialComplex)`
- barycentricSubdivision(SimplicialComplex,Ring) -- create the barycentric subdivision of a simplicial complex
- barycentricSubdivision(SimplicialMap,Ring,Ring) -- create the map between barycentric subdivisions corresponding to a simplicial map

## For the programmer

The object barycentricSubdivision is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ResolutionsOfStanleyReisnerRings.m2:329:0.