Here is an example of a full-rank vertex of $\hom(\Box_3, \Diamond_4)$, where $\Box_3$ is the unit cube in the positive orthant and $\Diamond_4$ is the standard 4D cross polytope (ie., with vertices at $\pm e_i$); the vertex is expressed in two ways:

v0*F11,v0*F15,
v1*F4,v1*F7,v1*F9,v1*F11,
v2*F4 ...

Can polymake express a vertex map of hom(p, q) explicitly as a map, i.e., as a linear-map-matrix and a shift vector?

Thank you!

This is great, thank you! Yes, $p is not a line segment; that was a typo on my part, as was the "[0, 1]" later in the post.

I'll pose this question using an example: I give Polymake a 2-cube ($p=cube(2)) and a line segment ($q=new Polytope<Rational>(POINTS=>new Matrix<Rational>([[1, 0], [0, 1]])), and then build the hom-polytope $hom=mapping_polytope($p, $q) and ask for its vertices. How can I determine which vertices ...

Thank you!

How do I have Polymake tell me the edges of a polytope? For example, print $p->VERTICES. "\n"; tells me the vertices of the polytope p. But print $p->EDGES. "\n"; doesn't do anything.