Results 1 to 10 of about 13,921 (178)
When can a net fold to a polyhedron?
Computational Geometry, 2005 AbstractIn this paper, we study the problem of whether a polyhedron can be obtained from a net by folding along the creases. We show that this problem can be solved in polynomial time if the dihedral angle at each crease is given, and it becomes NP-hard if these angles are unknown.
Julie Sun, Therese C. Biedl, Anna Lubiw
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Universal folding pathways of polyhedron nets [PDF]
Proceedings of the National Academy of Sciences, 2018 Significance What makes an object successful at thermal folding? Protein scientists study how sequence affects the pathways by which chained amino acids fold and the structures into which they fold. Here we investigate the inverse problem: Starting with a 3D object as a polyhedron we ask, which ones, among the many choices of 2D unfoldings ...
Pablo F. Damasceno +2 more
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Polyhedra, Complexes, Nets and Symmetry [PDF]
, 2014 Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial, and algebraic properties.
Schulte, Egon
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Finding the optimal nets for self-folding Kirigami [PDF]
, 2018 Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements.
Araújo, N. A. M. +3 more
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Basic nets in the projective plane [PDF]
, 2014 The notion of basic net (called also basic polyhedron) on $S^2$ plays a central role in Conway's approach to enumeration of knots and links in $S^3$. Drobotukhina applied this approach for links in $RP^3$ using basic nets on $RP^2$.
Orevkov, S. Yu.
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Elementary vectors and conformal sums in polyhedral geometry and their relevance for metabolic pathway analysis [PDF]
, 2016 A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have ...
Müller, Stefan, Regensburger, Georg
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Constructing chiral MOFs by functionalizing 4,2′:6′,4″-terpyridine with long-chain alkoxy domains: rare examples of neb nets [PDF]
, 2016 Reactions of 4′-(4- n alkyloxyphenyl)-4,2′:6′,4″-terpyridines (alkyl = hexyl or nonyl) with CoIJNCS) 2 lead to three structurally characterized chiral 3D assemblies which adopt rare neb topologies.
Coles, Simon +5 more
core +1 more source
Grid Vertex-Unfolding Orthogonal Polyhedra
, 2006 An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a *net*, a connected planar piece with no overlaps. A *grid unfolding* allows additional cuts along grid edges induced by coordinate planes passing through ...
Damian, Mirela +2 more
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Every Combinatorial Polyhedron Can Unfold with Overlap
, 2023 Ghomi proved that every convex polyhedron could be stretched via an affine transformation so that it has an edge-unfolding to a net [Gho14]. A net is a simple planar polygon; in particular, it does not self-overlap.
O'Rourke, Joseph
core
Mobility of a class of perforated polyhedra [PDF]
, 2016 A class of over-braced but typically flexible body-hinge frameworks is described. They are based on polyhedra with rigid faces where an independent subset of faces has been replaced by a set of holes.
Fowler, PW, Guest, SD, Schulze, B
core +4 more sources