Here we demonstrate the PolyMake wrappers Polytope and SimplicialComplex.

To use the Polytope domain we need to say

)lib STRCNV READFILE POLYTOPE

   StringConversions is now explicitly exposed in frame initial 
   StringConversions will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/STRCNV.NRLIB/STRCNV
   ReadFile is now explicitly exposed in frame initial 
   ReadFile will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/READFILE.NRLIB/READFILE
   Polytope is now explicitly exposed in frame initial 
   Polytope will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/POLYTOPE.NRLIB/POLYTOPE

To create a cube of dimension 4 and look at its h-vector, we say

c5 := cube 5

(1)

h5 := hVector c5

   >> Error detected within library code:
   End of file

The idea is to factor the h-polynomial, for example:

factor reduce(+, [h5.(i+1) * t^i for i in 0..#h5-1])

   There are 2 exposed and 2 unexposed library operations named # 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op #
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named # 
      with argument type(s) 
                                Variable(h5)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Of course, the cube is simple:

simple c5

   >> Error detected within library code:
   End of file

Here are its vertices:

vertices c5

   >> Error detected within library code:
   End of file

Here is a random polytope with 6 vertices on the 3-dimensional sphere

r5 := randSphere(3, 6)

(2)

Now vertices spits out a matrix containing the coordinates of the vertices of the polytope:

vertices r5

   >> Error detected within library code:
   End of file