Ununfoldable polyhedra with convex faces

DOI10.1016/S0925-7721(02)00091-3zbMath1021.52013OpenAlexW2148125855WikidataQ56970670 ScholiaQ56970670MaRDI QIDQ1869740

Yanyan Li

Publication date: 28 April 2003

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0925-7721(02)00091-3

zbMATH Keywords

treenetsdiscrete geometryedge unfoldingvertex unfoldingedge cuttingconvex closed polyhedronconvex unfoldingcuts across facesgeneral unfoldinggluing hats togethermiddle verticesopen convex-faced polyhedronpolyhedron with negative curvaturespike trianglespiked tetrahedrontopologically convex polyhedraunfolding polyhedra

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) Combinatorial complexity of geometric structures (52C45)

Related Items (16)

An algorithmic study of manufacturing paperclips and other folded structures. ⋮ Ununfoldable polyhedra with \(6\) vertices or \(6\) faces ⋮ Unfolding genus-2 orthogonal polyhedra with linear refinement ⋮ The material reasoning of folding paper ⋮ Toward unfolding doubly covered \(n\)-stars ⋮ Pseudo-edge unfoldings of convex polyhedra ⋮ Unfolding orthogonal polyhedra with quadratic refinement: the delta-unfolding algorithm ⋮ Unnamed Item ⋮ Continuous blooming of convex polyhedra ⋮ Unfolding polycube trees with constant refinement ⋮ Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings ⋮ When can a net fold to a polyhedron? ⋮ On polyhedral realization with isosceles triangles ⋮ Unfolding H-convex Manhattan towers ⋮ Unfolding \(3\)-separated polycube graphs of arbitrary genus ⋮ On the development of the intersection of a plane with a polytope

Uses Software

• UnfoldPolytope

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the development of closed convex curves on 3-polytopes
• Unsolved problems in geometry
• Nonoverlap of the star unfolding
• Enumerating foldings and unfoldings between polygons and polytopes
• The Discrete Geodesic Problem
• On Shortest Paths in Polyhedral Spaces
• Convex polytopes with convex nets
• Star Unfolding of a Polytope with Applications

This page was built for publication: Ununfoldable polyhedra with convex faces