<p><b>Abstract</b>—The main results of this paper are algorithms for time-optimal gossip of large packets in noncombining full-duplex all-port 2-D tori and meshes of any size <tmath>$m\times n$</tmath>. The gossip algorithms define the structure of broadcast trees and lock-step scheduling schemes for packets that make the broadcast trees time-arc-disjoint. The gossip algorithm for tori is also buffer-optimal—it requires routers with auxiliary buffers for at most three packets. The gossip algorithm for meshes requires routers with auxiliary buffers for <tmath>$O(m+n)$</tmath> packets.</p>