Volume 18, issue 5 (2014)

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Affine unfoldings of convex polyhedra

Mohammad Ghomi

Geometry & Topology 18 (2014) 3055–3090
Bibliography
1 A D Alexandrov, Convex polyhedra, Springer Monographs in Math., Springer (2005) MR2127379
2 V N Berestovskiĭ, C P Plaut, Covering $\mathbb{R}$–trees, $\mathbb{R}$–free groups and dendrites, Adv. Math. 224 (2010) 1765 MR2646109
3 M P do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Englewood Cliffs, N.J. (1976) MR0394451
4 H T Croft, K J Falconer, R K Guy, Unsolved problems in geometry, Problem Books in Math., Springer (1991) MR1107516
5 E D Demaine, M L Demaine, V Hart, J Iacono, S Langerman, J O’Rourke, Continuous blooming of convex polyhedra, Graphs Combin. 27 (2011) 363 MR2787423
6 E D Demaine, J O’Rourke, Geometric folding algorithms, Cambridge Univ. Press (2007) MR2354878
7 A Dürer, The painter's manual, Abaris Books (1977)
8 M Ghomi, Gauss map, topology and convexity of hypersurfaces with nonvanishing curvature, Topology 41 (2002) 107 MR1871243
9 M Ghomi, A Riemannian four vertex theorem for surfaces with boundary, Proc. Amer. Math. Soc. 139 (2011) 293 MR2729091
10 B Grünbaum, Nets of polyhedra, II, Geombinatorics 1 (1991) 5 MR1208436
11 B Grünbaum, No-net polyhedra, Geombinatorics 11 (2002) 111 MR1897413
12 J i Itoh, J O’Rourke, C Vîlcu, Star unfolding convex polyhedra via quasigeodesic loops, Discrete Comput. Geom. 44 (2010) 35 MR2639817
13 B Lucier, Local overlaps in special unfoldings of convex polyhedra, Comput. Geom. 42 (2009) 495 MR2512676
14 E Miller, I Pak, Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings, Discrete Comput. Geom. 39 (2008) 339 MR2383765
15 E E Moise, Geometric topology in dimensions $2$ and $3$, Graduate Texts in Math. 47, Springer (1977) MR0488059
16 J O’Rourke, How to fold it, Cambridge Univ. Press (2011) MR2768138
17 I Pak, Lectures on discrete and polyhedral geometry (2008)
18 C Schevon, Algorithms for geodesics on polytopes, PhD thesis, Johns Hopkins University (1989)
19 W Schlickenrieder, Nets of polyhedra, Master’s thesis, Technische Universität (1997)
20 G C Shephard, Convex polytopes with convex nets, Math. Proc. Cambridge Philos. Soc. 78 (1975) 389 MR0390915
21 M Spivak, A comprehensive introduction to differential geometry, Volume I, Publish or Perish, Inc. (1979) MR532830
22 A S Tarasov, Existence of a polyhedron which does not have a nonoverlapping pseudoedge unfolding, arXiv:0806.2360
23 G M Ziegler, Lectures on polytopes, Graduate Texts in Math. 152, Springer (1995) MR1311028