# Face -- The class of faces of simplicial complexes.

## Description

The class of faces of simplicial complexes on the variables of a polynomial ring. The faces are lists of variables of the PolynomialRing

The maximal faces can be obtained from a simplicial Complex by the method facets

 `i1 : K=QQ;` `i2 : R=K[x_0..x_4];` ```i3 : face {x_0,x_1} o3 = x x 0 1 o3 : face with 2 vertices``` ```i4 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0); o4 : Ideal of R``` ```i5 : D =idealToComplex I o5 = {x x , x x , x x , x x , x x } 2 4 0 3 0 2 1 3 1 4 o5 : complex with 5 facets on the vertices x x x x x 0 1 2 3 4``` ```i6 : fc=facets D o6 = {x x , x x , x x , x x , x x } 2 4 0 3 0 2 1 3 1 4 o6 : List``` ```i7 : fc#0 o7 = x x 2 4 o7 : face with 2 vertices```

• face -- Generate a face.
• idealToComplex -- Compute the Stanley-Reisner complex.
• Complex -- The class of all simplicial complexes.
• facets -- The facets of a simplicial complex.
• faces -- Returns the faces of a complex

## Methods that use an object of class Face :

• dimension(Face), see dimension -- The dimension of a simplicial complex or a face of a simplicial complex.
• Face == Face -- Compare two faces.
• faceIdeal(Face), see faceIdeal -- The ideal of a face of a simplicial complex.
• isFace(Face,Complex), see isFace -- Test whether a face is a face of a given complex.
• isSubface(Face,Face), see isSubface -- Test whether a face is a subface of another face.