@techreport{oai:ipsj.ixsq.nii.ac.jp:00095744,
 author = {ZacharyR.Abel and ErikD.Demaine and MartinL.Demaine and Hiro, Ito and Jack, Snoeyink and Ryuhei, Uehara and Zachary, R.Abel and Erik, D.Demaine and Martin, L.Demaine and Hiro, Ito and Jack, Snoeyink and Ryuhei, Uehara},
 issue = {19},
 month = {Oct},
 note = {Folding problems are investigated for a class of petal (or star-like) polygons P, with an n-polygonal base B surrounded by a sequence of triangles for which adjacent pairs of sides have equal length. Linear time algorithms using constant precision are given to determine if P can fold to a pyramid with flat base B, and to determine a triangulation of B (crease pattern) that allows folding into a bumpy pyramid that is convex. By Alexandrov's theorem, the crease pattern is unique if it exists, but the general algorithm known for this theorem is pseudo-polynomial, with very large running time; ours is the first efficient algorithm for Alexandrov's theorem for a special class of polyhedra. We also show a polynomial time algorithm that finds the crease pattern to produce the maximum volume bumpy pyramid., Folding problems are investigated for a class of petal (or star-like) polygons P, with an n-polygonal base B surrounded by a sequence of triangles for which adjacent pairs of sides have equal length. Linear time algorithms using constant precision are given to determine if P can fold to a pyramid with flat base B, and to determine a triangulation of B (crease pattern) that allows folding into a bumpy pyramid that is convex. By Alexandrov's theorem, the crease pattern is unique if it exists, but the general algorithm known for this theorem is pseudo-polynomial, with very large running time; ours is the first efficient algorithm for Alexandrov's theorem for a special class of polyhedra. We also show a polynomial time algorithm that finds the crease pattern to produce the maximum volume bumpy pyramid.},
 title = {Bumpy Pyramid Folding Problem},
 year = {2013}
}