Grassmannian-parameterized solutions to direct-sum polygon and simplex equations

We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) Yang–Baxter (2-simplex), respectively. examine general structure (2n + 1)-gon 2n-simplex equations in direct sums vector spaces. Then, we provide a construction for their solutions, parameterized by elements Grassmannian Gr(n 1, 2n 1).