How to define Newton polytopes of a list of polynomials and compute the vertices, rays?

[lijr07]

I have a list of polynomials 1+x, x, 1+x*y+x, x+x*y, x*y, and would like to define the Newton polytope of the polynomials and compute the vertices and rays of the polytope. How to do this in polymake? Thank you very much.

[joswig]

A google search for "polymake" and "newton polytope" reveals:
https://polymake.org/doku.php/user_guid ... s_tutorial