Face -- The class of faces of simplicial complexes.

i1 : R=QQ[x_0..x_4];

i2 : F=face {x_0,x_2}

o2 = x  x  
      0  2

o2 : face with 2 vertices in R

i3 : vertices F

o3 = {x , x }
       0   2

o3 : List

i4 : I = monomialIdeal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0);

o4 : MonomialIdeal of R

i5 : D = simplicialComplex I

o5 = simplicialComplex | x_2x_4 x_1x_4 x_1x_3 x_0x_3 x_0x_2 |

o5 : SimplicialComplex

i6 : fc = faces(1, D)

o6 = {x x , x x , x x , x x , x x }
       0 2   0 3   1 3   1 4   2 4

o6 : List

Functions and methods returning an object of class Face :

• face(List) -- see face -- Generate a face.
• face(List,PolynomialRing) -- see face -- Generate a face.

Methods that use an object of class Face :

• dim(Face) -- The dimension of a face.
• Face == Face -- Compare two faces.
• isSubface(Face,Face) -- see isSubface -- Test whether a face is a subface of another face.
• net(Face) -- Printing a face.
• ring(Face) -- Ring of a face.
• stellarSubdivision(SimplicialComplex,Face,PolynomialRing) -- see stellarSubdivision -- Compute the stellar subdivision of a simplicial complex.
• substitute(Face,PolynomialRing) -- Substitute a face to a different ring.
• vertices(Face) -- The vertices of a face of a simplicial complex.

For the programmer

The object Face is a type, with ancestor classes MutableHashTable < HashTable < Thing.