منابع مشابه
Continuous Blooming of Convex Polyhedra
We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.
متن کاملRefold rigidity of convex polyhedra
We show that every convex polyhedron may be unfolded to one planar piece, and then refolded to a different convex polyhedron. If the unfolding is restricted to cut only edges of the polyhedron, we identify several polyhedra that are “edge-unfold rigid” in the sense that each of their unfoldings may only fold back to the original. For example, each of the 43,380 edge unfoldings of a dodecahedron...
متن کاملAffine Unfoldings of Convex Polyhedra
We show that every convex polyhedron admits a simple edge unfolding after an affine transformation. In particular there exists no combinatorial obstruction to a positive resolution of Dürer’s unfoldability problem, which answers a question of Croft, Falconer, and Guy. Among other techniques, the proof employs a topological characterization for embeddings among the planar immersions of the disk.
متن کاملSpiral Unfoldings of Convex Polyhedra
The notion of a spiral unfolding of a convex polyhedron, resulting by flattening a special type of Hamiltonian cut-path, is explored. The Platonic and Archimedian solids all have nonoverlapping spiral unfoldings, although among generic polyhedra, overlap is more the rule than the exception. The structure of spiral unfoldings is investigated, primarily by analyzing one particular class, the poly...
متن کاملDetecting intersections between convex polyhedra
For a polyhedron P in R, denote by |P | its combinatorial complexity, i.e., the number of faces, edges and vertices of the polyhedra. In this paper, we revisit the classic problem of preprocessing polyhedra independently so that given two preprocessed polyhedra P and Q in R, each translated and rotated, their intersection can be tested rapidly. For d = 3 we show how to perform such a test in O(...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2011
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-011-1024-3