Add to ORKGThe notion of a spiral unfolding of a convex polyhedron, a special type of Hamiltonian cut-path, is explored. The Platonic and Archimedian solids all have nonoverlapping spiral unfoldings, although overlap is more the rule than the exception among generic polyhedra. The structure of spiral unfoldings is described, primarily through analyzing one particular class, the polyhedra of revolution.
We prove that an infinite class of convex polyhedra, produced by restricted vertex truncations, alwa...
AbstractWe define a notion of local overlaps in polyhedron unfoldings. We use this concept to constr...
It is shown that there are examples of distinct polyhedra, each with a Hamiltonian path of edges, wh...
We explore which polyhedra and polyhedral complexes can be formed by folding up a planar polygonal r...
We explore which polyhedra and polyhedral complexes can be formed by folding up a planar polygonal ...
We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfo...
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
We show that four of the five Platonic solids ’ surfaces may be cut open with a Hamiltonian path alo...
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
It is a common conjecture that all convex polyhedra must be edge-unfoldable but to date a valid proo...
We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygona...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected ...
This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra a...
We prove that an infinite class of convex polyhedra, produced by restricted vertex truncations, alwa...
We prove that an infinite class of convex polyhedra, produced by restricted vertex truncations, alwa...
AbstractWe define a notion of local overlaps in polyhedron unfoldings. We use this concept to constr...
It is shown that there are examples of distinct polyhedra, each with a Hamiltonian path of edges, wh...
We explore which polyhedra and polyhedral complexes can be formed by folding up a planar polygonal r...
We explore which polyhedra and polyhedral complexes can be formed by folding up a planar polygonal ...
We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfo...
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
We show that four of the five Platonic solids ’ surfaces may be cut open with a Hamiltonian path alo...
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
It is a common conjecture that all convex polyhedra must be edge-unfoldable but to date a valid proo...
We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygona...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected ...
This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra a...
We prove that an infinite class of convex polyhedra, produced by restricted vertex truncations, alwa...
We prove that an infinite class of convex polyhedra, produced by restricted vertex truncations, alwa...
AbstractWe define a notion of local overlaps in polyhedron unfoldings. We use this concept to constr...
It is shown that there are examples of distinct polyhedra, each with a Hamiltonian path of edges, wh...