Let {a, b, c} be a triangle in a 3-connected matroid M. In this paper, we describe the structure of M relative to {a, b, c} when, for all t in {a, b, c}, either M is not 3-connected, or M has a 3-separation that is not equivalent to one induced by M. (C) 2007 Elsevier Inc. All rights reserved.
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