Here we demonstrate the PolyMake wrappers Polytope and SimplicialComplex.

To use the Polytope domain we need to say

(1) -> )lib STRCNV READFILE POLYTOPE

   >> System error:
   The value
  1954
is not of type
  LIST

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

c5 := cube 5

   There are no library operations named cube 
      Use HyperDoc Browse or issue
                                )what op cube
      to learn if there is any operation containing " cube " in its 
      name.

   Cannot find a definition or applicable library operation named cube 
      with argument type(s) 
                               PositiveInteger

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

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

   There are no library operations named simple 
      Use HyperDoc Browse or issue
                               )what op simple
      to learn if there is any operation containing " simple " in its 
      name.

   Cannot find a definition or applicable library operation named 
      simple with argument type(s) 
                                Variable(c5)

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

Here are its vertices:

vertices c5

   There are no library operations named vertices 
      Use HyperDoc Browse or issue
                              )what op vertices
      to learn if there is any operation containing " vertices " in its
      name.

   Cannot find a definition or applicable library operation named 
      vertices with argument type(s) 
                                Variable(c5)

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

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

r5 := randSphere(3, 6)

   There are no library operations named randSphere 
      Use HyperDoc Browse or issue
                             )what op randSphere
      to learn if there is any operation containing " randSphere " in 
      its name.

   Cannot find a definition or applicable library operation named 
      randSphere with argument type(s) 
                               PositiveInteger
                               PositiveInteger

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

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

vertices r5

   There are no library operations named vertices 
      Use HyperDoc Browse or issue
                              )what op vertices
      to learn if there is any operation containing " vertices " in its
      name.

   Cannot find a definition or applicable library operation named 
      vertices with argument type(s) 
                                Variable(r5)

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