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16
Band Unfoldings and Prismatoids: A Counterexample
, 2007
"... This note shows that the hope expressed in [ADL + 07]—that the new algorithm for edgeunfolding any polyhedral band without overlap might lead to an algorithm for unfolding any prismatoid without overlap—cannot be realized. A prismatoid is constructed whose sides constitute a nested polyhedral band, ..."
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This note shows that the hope expressed in [ADL + 07]—that the new algorithm for edgeunfolding any polyhedral band without overlap might lead to an algorithm for unfolding any prismatoid without overlap—cannot be realized. A prismatoid is constructed whose sides constitute a nested polyhedral band
Unfolding Prismatoids as Convex Patches: Counterexamples and Positive Results
, 2012
"... We address the unsolved problem of unfolding prismatoids in a new context, viewing a “topless prismatoid” as a convex patch—a polyhedral subset of the surface of a convex polyhedron homeomorphic to a disk. We show that several natural strategies for unfolding a prismatoid can fail, but obtain a pos ..."
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Cited by 2 (1 self)
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We address the unsolved problem of unfolding prismatoids in a new context, viewing a “topless prismatoid” as a convex patch—a polyhedral subset of the surface of a convex polyhedron homeomorphic to a disk. We show that several natural strategies for unfolding a prismatoid can fail, but obtain a
Unfolding Polyhedral Bands
"... A band is de ned as the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. An unfolding of a given band is obtained by cutting along exactly one edge and placing all faces of the band ..."
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Cited by 3 (2 self)
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A band is de ned as the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. An unfolding of a given band is obtained by cutting along exactly one edge and placing all faces of the band
EdgeUnfolding Nested Polyhedral Bands
, 2006
"... A band is the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. The intersection of the planes and the polyhedron produces two convex polygons. If one of these polygons contains the ot ..."
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Cited by 4 (3 self)
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the other in the projection orthogonal to the parallel planes, then the band is nested. We prove that all nested bands can be unfolded, by cutting along exactly one edge and folding continuously to place all faces of the band into a plane, without intersection.
Zipper Unfolding of Domes and Prismoids
"... We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfold it without overlap—of two classes of polyhedra. Such unfoldings could be implemented by a single zipper, so they are also known as zipper edge unfoldings. First we consider domes, which are simple ..."
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We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfold it without overlap—of two classes of polyhedra. Such unfoldings could be implemented by a single zipper, so they are also known as zipper edge unfoldings. First we consider domes, which are simple
Zipper Unfolding of Domes and Prismoids
, 2013
"... We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfold it without overlap—of two classes of polyhedra. Such unfoldings could be implemented by a single zipper, so they are also known as zipper edge unfoldings. First we consider domes, which are simple ..."
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Cited by 1 (0 self)
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We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfold it without overlap—of two classes of polyhedra. Such unfoldings could be implemented by a single zipper, so they are also known as zipper edge unfoldings. First we consider domes, which are simple
The Star Unfolding from a Geodesic Curve
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii An unfolding of a polyhedron P is obtained by ‘cutting ..."
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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii An unfolding of a polyhedron P is obtained
A Class of Convex Polyhedra with Few Edge Unfoldings
, 2008
"... We construct a sequence of convex polyhedra on n vertices with the property that, as n→∞, the fraction of its edge unfoldings that avoid overlap approaches 0, and so the fraction that overlap approaches 1. Nevertheless, each does have (several) nonoverlapping edge unfoldings. ..."
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Cited by 1 (1 self)
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We construct a sequence of convex polyhedra on n vertices with the property that, as n→∞, the fraction of its edge unfoldings that avoid overlap approaches 0, and so the fraction that overlap approaches 1. Nevertheless, each does have (several) nonoverlapping edge unfoldings.
A Class of Convex Polyhedra
"... We construct a sequence of convex polyhedra on n vertices with the property that, as n→∞, the fraction of its edge unfoldings that avoid overlap approaches 0, and so the fraction that overlap approaches 1. Nevertheless, each does have (several) nonoverlapping edge unfoldings. 1 ..."
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We construct a sequence of convex polyhedra on n vertices with the property that, as n→∞, the fraction of its edge unfoldings that avoid overlap approaches 0, and so the fraction that overlap approaches 1. Nevertheless, each does have (several) nonoverlapping edge unfoldings. 1
Results 1  10
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16