complexFromFacets -- Make a complex from its facets.

i1 : R=QQ[x_0..x_5]

o1 = R

o1 : PolynomialRing

i2 : C=boundaryCyclicPolytope(3,R)

o2 = 2: x x x  x x x  x x x  x x x  x x x  x x x  x x x  x x x  
         0 1 2  0 2 3  0 3 4  0 1 5  1 2 5  2 3 5  0 4 5  3 4 5

o2 : complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1

i3 : fC=facets C

o3 = {{}, {}, {}, {x x x , x x x , x x x , x x x , x x x , x x x , x x x , x x x }, {}, {}, {}}
                    0 1 2   0 2 3   0 3 4   0 1 5   1 2 5   2 3 5   0 4 5   3 4 5

o3 : List

i4 : C1=complexFromFacets(R,fC)

o4 = 2: x x x  x x x  x x x  x x x  x x x  x x x  x x x  x x x  
         0 1 2  0 2 3  0 3 4  0 1 5  1 2 5  2 3 5  0 4 5  3 4 5

o4 : complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial

i5 : C1==C

o5 = true

i6 : fc C1;

i7 : C1

o7 = 2: x x x  x x x  x x x  x x x  x x x  x x x  x x x  x x x  
         0 1 2  0 2 3  0 3 4  0 1 5  1 2 5  2 3 5  0 4 5  3 4 5

o7 : complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1