link -- The link of a face of a complex.

i1 : R=QQ[x_0..x_4]

o1 = R

o1 : PolynomialRing

i2 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)

o2 = ideal (x x , x x , x x , x x , x x )
             0 1   1 2   2 3   3 4   0 4

o2 : Ideal of R

i3 : C=idealToComplex I

o3 = {x  x  , x  x  , x  x  , x  x  , x  x  }
       2  4    0  3    0  2    1  3    1  4

o3 : complex with 5 facets on the vertices x  x  x  x  x  
                                            0  1  2  3  4

i4 : F=(faces C)#1#0

o4 = x  
      1

o4 : face with 1 vertices

i5 : link(F,C)

o5 = {x  , x  }
       3    4

o5 : complex with 2 facets on the vertices x  x  x  x  x  
                                            0  1  2  3  4

i6 : F=(faces C)#2#0

o6 = x  x  
      1  4

o6 : face with 2 vertices

i7 : link(F,C)

o7 = {{}}

o7 : empty complex