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To get a matrix, you can do

sage: L = polytopes.dodecahedron().face_lattice()
sage: L.hasse_diagram().adjacency_matrix()
64 x 64 dense matrix over Integer Ring (use the '.str()' method to see the entries)

and if you want to get rid of the empty face before, you can use

sage: L = L.subposet([f for f in L if f.dimension()>=0])