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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract-We study an interconnection network that we call 3T orus(m, n) obtained by pruning the 4m × 4n torus (of links) so that the resulting network is regular of degree 3. We show that 3T orus(m, n) retains many of the useful properties of tori (although, of course, there is a price to be paid due to the reduction in links). In particular: we show that 3T orus(m, n) is node-symmetric; we establish closedform expressions on the the length of a shortest path joining any two nodes of the network; we calculate the diameter precisely; we obtain an upper bound on the average internode distance; we develop an optimal distributed routing algorithm; we prove that 3T orus(m, n) has connectivity 3 and is Hamiltonian; we obtain a precise expression for (an upper bound on) the wide-diameter; and we derive optimal one-toall broadcast and personalized one-to-all broadcast algorithms under both a one-port and all-port communication model. We also undertake a preliminary performance evaluation of our routing algorithm. In summary, we find that 3T orus(m, n) compares very favourably with tori.