Add to ORKGThe combinatorial, geometric, and topological structure of the set of all convex polyhedra foldable from a square is detailed. It is proved that five combinatorially distinct nondegenerate polyhedra, and four different flat polyhedra, are realizable. All the polyhedra are continuously deformable into each other, with the space of polyhedra forming four connected rings.
We study the problem of folding a polyomino P into a polycube Q, allowing faces of Q to be covered m...
A folding of a simple polygon into a convex polyhedron is accomplished by glueing portions of the pe...
It is known that one can fold a convex polyhedron from a non-overlapping face unfolding, but the com...
The structure of the set of all convex polyhedra foldable from a square is detailed. It is proved th...
We give a complete description of all convex polyhedra whose surface can be constructed from several...
We prove that each Platonic polyhedron P can be folded into a flat multilayered face of P by a conti...
AbstractUnfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In thi...
Mathematicians have long been asking the question: Can a given convex polyhedron can be unfolded int...
A well-known problem in geometry, which may be traced back to the Renaissance artist Albrecht Durer,...
This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra a...
We show that the open problem presented in Geometric Folding Algo-rithms: Linkages, Origami, Polyhed...
We show that every convex polyhedron may be unfolded to one planar piece, and then refolded to a dif...
Abstract. We show that every convex polyhedron admits a simple edge unfold-ing after an affine trans...
AbstractThe best-known developments of a regular tetrahedron are an equilateral triangle and a paral...
Which convex 3D polyhedra can be obtained by gluing several regular hexagons edge-to-edge? It turns ...
We study the problem of folding a polyomino P into a polycube Q, allowing faces of Q to be covered m...
A folding of a simple polygon into a convex polyhedron is accomplished by glueing portions of the pe...
It is known that one can fold a convex polyhedron from a non-overlapping face unfolding, but the com...
The structure of the set of all convex polyhedra foldable from a square is detailed. It is proved th...
We give a complete description of all convex polyhedra whose surface can be constructed from several...
We prove that each Platonic polyhedron P can be folded into a flat multilayered face of P by a conti...
AbstractUnfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In thi...
Mathematicians have long been asking the question: Can a given convex polyhedron can be unfolded int...
A well-known problem in geometry, which may be traced back to the Renaissance artist Albrecht Durer,...
This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra a...
We show that the open problem presented in Geometric Folding Algo-rithms: Linkages, Origami, Polyhed...
We show that every convex polyhedron may be unfolded to one planar piece, and then refolded to a dif...
Abstract. We show that every convex polyhedron admits a simple edge unfold-ing after an affine trans...
AbstractThe best-known developments of a regular tetrahedron are an equilateral triangle and a paral...
Which convex 3D polyhedra can be obtained by gluing several regular hexagons edge-to-edge? It turns ...
We study the problem of folding a polyomino P into a polycube Q, allowing faces of Q to be covered m...
A folding of a simple polygon into a convex polyhedron is accomplished by glueing portions of the pe...
It is known that one can fold a convex polyhedron from a non-overlapping face unfolding, but the com...