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Tech. Rep. 797, Computer Science Department, Technion, Israel Inst. , 1994. [15] H. Koike, An application of three-dimensional visualization to objectoriented programming. In T. Catarci, M. F. Costabile, and S. , Proc. Advanced Visual Interfaces (AVI ’92), vol. 36 of Series in Comput. , pp. 180–192, World Scientific, 1992. [16] H. Koike, The role of another spatial dimension in software visualization. ACM Trans. Inf. , 11(3):266–286, 1993. [17] A. N. Kolmogorov and Y. M. Barzdin, On the realization of nets in 3-dimensional space.

Patrignani, and F. Vargiu, A split&push approach to 3D orthogonal drawing. J. , 4(3):105– 133, 2000. [12] P. Eades, C. Stirk, and S. Whitesides, The techniques of Kolmogorov and Barzdin for three dimensional orthogonal graph drawings. Inform. Proc. , 60(2):97–103, 1996. [13] P. Eades, A. Symvonis, and S. Whitesides, Three dimensional orthogonal graph drawing algorithms. , 103:55–87, 2000. D. Wood, Lower Bounds for 3-D Drawings, JGAA, 7(1) 33–77 (2003) 67 [14] S. Even and G. Granot, Rectilinear planar drawings with few bends in each edge.

Lemma 5. If a drawing of K7 contains a 0-bend 7-cycle then there are at least six chords of the cycle each with at least three bends. Proof. By Observation 2, a 0-bend drawing of C7 has four, six or seven sides. In a 4-sided 0-bend drawing of C7 , as illustrated in Figure 12, the three vertices not at the intersection of two adjacent sides can be (a) all on the same side, (b) two on one side and one on an adjacent side, (c) two on one side and one on the opposite side, or (d) all on different sides.

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