# convHull -- The convex hull complex.

## Synopsis

• Usage:
convHull(L)
convHull(fn)
• Inputs:
• Optional inputs:
• file => ..., default value null, Store result of a computation in a file.
• Outputs:
• C, ,

## Description

Returns the convex hull of lattice vectors lying all in the same space. The output has C.isPolytope==true.

If applied to the string fn the result of a previous computation stored via the option file is read from the file fn.

The 0-point has to lie in the convex hull.

 i1 : L={vector {1,0,0},vector {-1,0,0},vector {0,1,0},vector {0,-1,0},vector {0,0,1},vector {0,0,-1}} o1 = {| 1 |, | -1 |, | 0 |, | 0 |, | 0 |, | 0 |} | 0 | | 0 | | 1 | | -1 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 1 | | -1 | o1 : List i2 : P=convHull(L) o2 = 3: y y y y y y 0 1 2 3 4 5 o2 : complex of dim 3 embedded in dim 3 (printing facets) equidimensional, non-simplicial, F-vector {1, 6, 12, 8, 1}, Euler = 0 i3 : dP=boundaryOfPolytope P o3 = 2: y y y y y y y y y y y y y y y y y y y y y y y y 0 2 4 1 2 4 0 3 4 1 3 4 0 2 5 1 2 5 0 3 5 1 3 5 o3 : complex of dim 2 embedded in dim 3 (printing facets) equidimensional, simplicial, F-vector {1, 6, 12, 8, 0}, Euler = 1

## Caveat

This uses the package OldPolyhedra.m2 to compute the facets. Too slow compared to Maple/convex.

If the package ConvexInterface is loaded, then this command calls Maple/Convex. See the corresponding option explained at SRdeformations.