Here we demonstrate the PolyMake wrappers `Polytope`

and `SimplicialComplex`

.

To use the `Polytope`

domain we need to say

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)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

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c5 := cube 5

**Type: **Polytope

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h5 := hVector c5

>> Error detected within library code:
End of file

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

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

There are 2 exposed and 1 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:

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simple c5

>> Error detected within library code:
End of file

Here are its vertices:

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vertices c5

>> Error detected within library code:
End of file

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

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r5 := randSphere(3, 6)

**Type: **Polytope

Now `vertices`

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

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vertices r5

>> Error detected within library code:
End of file