# complexFromFacets -- Make a complex from its facets.

## Synopsis

• Usage:
complexFromFacets(R,facetlist)
complexFromFacets(R,facetlist,Rdual)
• Inputs:
• R, ,
• facetlist, a list, of the facets, sorted by dimension
• Rdual, ,
• Outputs:
• ,

## Description

Make a complex from a list of faces and/or facets.

This is mostly used internally but may be occasionally useful for the end user.

 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 , 0 1 2 0 2 3 0 3 4 0 1 5 1 2 5 2 3 5 0 4 5 ------------------------------------------------------------------------ x x x }, {}, {}, {}} 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

## Caveat

If both the list of faces and facets is specified there is no consistency check.