  We describe an elementary convex geometric algorithm for realizing Schubert
cycles in complete flag varieties by unions of faces of polytopes. For GL_n and
Gelfand--Zetlin polytopes, combinatorics of this algorithm coincides with that
of the mitosis on pipe dreams introduced by Knutson and Miller. For Sp_4 and a
Newton--Okounkov polytope of the symplectic flag variety, the algorithm yields
a new combinatorial rule that extends to Sp_{2n}.
