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