An unfolding of a polyhedron along its edges is called a vertex unfolding if adjacent faces are allowed to be connected at not only an edge but also a vertex. Demaine et al [1] showed that every triangulated polyhedron has a vertex unfolding. We extend this result to a tight polyhedron, where a polyhedron is tight if its non-triangular faces are mutually non-incident.

An integer packing set is a of non-negative vectors with the property that, if vector x in set, then every y y≤x as well. The main result this paper that sets, ordered by inclusion, form well-quasi-ordering. This allows us to answer recently posed question: k-aggregation closure any polyhedron again polyhedron.

Weidong Min Abstract. This paper presents an algorithm based on shrunken polyhedron and mapping to mesh a convex polyhedron using mixed elements, with mostly hexahedra, but including some tetrahedra, pyramids, and wedges. It is part of a scheme for automatically meshing an arbitrary 3D geometry. The scheme rst decomposes a 3D geometry into a set of convex polyhedra. Then the boundary quadrilate...

Euler’s polyhedron formula asserts for a polyhedron p that

Given a set M ⊂ Z, an enclosing polyhedron for M is any polyhedron P such that the set of integer points contained in P is precisely M . Representing a discrete volume by enclosing polyhedron is a fundamental problem in visualization. In this paper we propose the first proof of the long-standing conjecture that the problem of finding an enclosing polyhedron with a minimal number of 2-facets is ...

We describe a new approach to fit the polyhedron describing a 3D building model to the point cloud of a Digital Elevation Model (DEM). We introduce a new kinetic framework that hides to its user the combinatorial complexity of determining or maintaining the polyhedron topology, allowing the design of a simple variational optimization. This new kinetic framework allows the manipulation of a boun...

Intersection cuts were introduced by Balas and the corner polyhedron by Gomory. Balas showed that intersection cuts are valid for the corner polyhedron. In this paper we show that, conversely, every nontrivial facet-defining inequality for the corner polyhedron is an intersection cut.