Constructing a 3-tree for a 3-connected matroid

Cook, 1998 W.H. Cunningham, A combinatorial decomposition theory, PhD thesis, University of Waterloo, 1973. Edmonds, 1970, Submodular functions, matroids and certain polyhedra, 69 Oxley, 2011 Oxley, 2004, The structure of the 3-separations of 3-connected matroids, J. Combin. Theory Ser. B, 92, 257, 10.1016/j.jctb.2004.03.006 Oxley, 2007, The structure of the 3-separations of 3-connected matroids, II, European J. Combin., 28, 1239, 10.1016/j.ejc.2006.01.007 Oxley, 2012, An upgraded Wheels-and-Whirls Theorem for 3-connected matroids, J. Combin. Theory Ser. B, 102, 610, 10.1016/j.jctb.2011.09.005