It is known that one can fold a convex polyhedron from a non-overlapping face unfolding, but the complexity of the algorithm in [MP] remains an open prob-lem. In this paper we show that every convex polyhedron P ⊂ Rd can be obtained in polynomial time, by starting with a cube which contains P and sequentially cutting out the extra parts of the surface. Our main tool is of independent interest. We prove that given a convex polytope P in Rd and a facet F of P, F is contained in the union ∪G 6=FΦF,G(G). The union is over all the facets G of P different from F and ΦF,G(G) is the set obtained from G by rotating the hyperplane which contains G about the intersection of it with the hyperplane which contains F until they coincide
Abstract. Recent progress is described on the unsolved problem of unfolding the surface of an orthog...
Introduction We present a locality-based algorithm to solve the problem of splitting a complex of c...
It is a common conjecture that all convex polyhedra must be edge-unfoldable but to date a valid proo...
AbstractUnfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In thi...
A well-known problem in geometry, which may be traced back to the Renaissance artist Albrecht Durer,...
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper,...
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper,...
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected ...
AbstractUnfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In thi...
AbstractA face-cycle of a polyhedron in R3 is a cyclic sequence of at least three, distinct faces of...
We give a complete description of all convex polyhedra whose surface can be constructed from several...
We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triang...
We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygona...
The main result of this paper is a proof that a nearly flat, acutely triangulated convex cap C in ℝ3...
We show that cutting shortest paths from every vertex of a convex polyhedron to a simple closed quas...
Abstract. Recent progress is described on the unsolved problem of unfolding the surface of an orthog...
Introduction We present a locality-based algorithm to solve the problem of splitting a complex of c...
It is a common conjecture that all convex polyhedra must be edge-unfoldable but to date a valid proo...
AbstractUnfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In thi...
A well-known problem in geometry, which may be traced back to the Renaissance artist Albrecht Durer,...
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper,...
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper,...
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected ...
AbstractUnfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In thi...
AbstractA face-cycle of a polyhedron in R3 is a cyclic sequence of at least three, distinct faces of...
We give a complete description of all convex polyhedra whose surface can be constructed from several...
We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triang...
We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygona...
The main result of this paper is a proof that a nearly flat, acutely triangulated convex cap C in ℝ3...
We show that cutting shortest paths from every vertex of a convex polyhedron to a simple closed quas...
Abstract. Recent progress is described on the unsolved problem of unfolding the surface of an orthog...
Introduction We present a locality-based algorithm to solve the problem of splitting a complex of c...
It is a common conjecture that all convex polyhedra must be edge-unfoldable but to date a valid proo...
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