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An approach to local area network interconnection is presented Which combines the advances in static interconnection topologies, demand assignment multiple access protocols, and the availability of high-bandwidth fiber optic channels to create a cost-effective structure capable of interconnecting a large number of LAN's with heavy traffic. This approach is independent of the protocol implemented at each LAN. The structure is based on a hypercube topology where each vertex of the graph represents a LAN. Multiple access channels spanning all dimensional axes are used in this scheme. This approach is compared to a topology with direct point-to-point connections between all nodes sharing a common axis. Through the development of the degree, diameter, average distance, cost, and average packet delay, we show that using fewer high-capacity channels, a LAN interconnection network with excellent performance characteristics can be constructed, able to support a large number of LAN's with heavy traffic at a significant reduction in cost over the point-to-point case. The resulting structure has many of the desirable characteristics for static interconnection networks such as high fault tolerance, totally distributed packet routing in the interconnection network, low average distance for good performance, and low degree, resulting in low cost. For the total number of required LAN nodes and the expected amount of internode traffic, the structure is optimized for minimum cost.