  The problem of existence of nontrivial Massey products in cohomology of a
space is well-known in algebraic topology and homological algebra. A number of
problems in complex geometry, symplectic geometry, and algebraic topology can
be stated in terms of Massey products. One of such problems is to establish
formality of smooth manifolds in rational homotopy theory. There have already
been constructed a few classes of spaces with nontrivial triple Massey products
in cohomology. Until now, very few examples of manifolds $M$ with nontrivial
higher Massey products in $H^*(M)$ were known. In this work we introduce a
sequence of smooth closed manifolds $\{M_{k}\}^{\infty}_{k=1}$ such that
$M_{k}\hookrightarrow M_{k+1}$ is a submanifold and a retract of $M_{k+1}$ for
any $k\geq 1$ and there exists a nontrivial Massey product
$\langle\alpha_{1},\ldots,\alpha_{n}\rangle$ in $H^*(M_{k})$ for each $2\leq
n\leq k$. The sequence $\{M_k\}^{\infty}_{k=1}$ is determined by a new family
of flag nestohedra $\mathcal P_{Mas}$. We give P.D.E. for the two-parametric
generating series of $\mathcal P_{Mas}$.
