  An approach to Schubert calculus is to realize Schubert classes as concrete
combinatorial objects such as Schubert polynomials. Using the polytope ring of
the Gelfand-Tsetlin polytopes, Kiritchenko-Smirnov-Timorin realized each
Schubert class as a sum of reduced Kogan faces. The first named author
introduced a generalization of reduced Kogan faces to symplectic
Gelfand-Tsetlin polytopes using a semi-toric degeneration of a Schubert
variety, and extended the result of Kiritchenko-Smirnov-Timorin to type C case.
In this paper, we introduce a combinatorial model to this type C generalization
using a kind of pipe dream with self-crossings. As an application, we prove
that the type C generalization can be constructed by skew mitosis operators.
