subword complexes are simplicial complexes introduced by knutson and miller to illustrate the combinatorics of schubert polynomials and determinantal ideals. they proved that any subword complex is homeomorphic to a ball or a sphere and asked about their geometric realizations. we show that a family of subword complexes can be realized geometrically via triangulations of root polytopes. this implies that a family of $beta$-grothendieck polynomials are special cases of reduced forms in the subdivision algebra of root polytopes. based on joint work with laura escobar.