Secure multiparty computation (MPC) allows a set of parties to jointly compute a function while keeping their inputs private. Classical MPC protocols assume either a synchronous or an asynchronous network. Synchronous protocols tolerate more corrupted parties but rely on a timing bound, while asynchronous protocols make no timing assumptions but handle fewer corruptions. The network-agnostic model aims to combine the advantages of both. It requires security without knowing in advance whether the network is synchronous or asynchronous, guaranteeing resilience against up to \(t_s\) corruptions in the synchronous case and \(t_a\) corruptions in the asynchronous case. The optimal corruption threshold for perfect security has been established as \(n = 2\max (t_s, t_a) + \max (2t_a, t_s) + 1\) , but prior work either falls short of this threshold or requires exponential local computation. In this work, we present the first perfectly secure network-agnostic MPC protocol with polynomial communication and computation complexity under the optimal threshold. Our protocol achieves expected communication complexity \(\mathcal {O}((|C|n + (D+C_I)n^2 + n^6)\log n)\) bits for a circuit of size |C| over a finite field \(\mathbb {F}\) of size \(\mathcal {O}(n)\) , depth D, and input size \(C_I\) . Our main technical contribution is a compiler that generates Beaver triples in the network-agnostic setting using synchronous and asynchronous triple-generation protocols in a black-box way. Beyond the cost of the underlying protocols, it only requires \(\mathcal {O}(n^2)\) instances of network-agnostic Byzantine agreement.