• Corpus ID: 233481826

Edge-unfolding nested prismatoids

@inproceedings{Radons2021EdgeunfoldingNP,
  title={Edge-unfolding nested prismatoids},
  author={Manuel Radons},
  year={2021}
}
A 3-Prismatoid is the convex hull of two convex polygons A and B which lie in parallel planes HA, HB ⊂ R . Let A be the orthogonal projection of A onto HB. A prismatoid is called nested if A ′ is properly contained in B, or vice versa. We show that every nested prismatoid has an edge-unfolding to a non-overlapping polygon in the plane. 1 

Figures from this paper

References

SHOWING 1-10 OF 24 REFERENCES
Stacked
Acutely Triangulated, Stacked, and Very Ununfoldable Polyhedra
We present new examples of topologically convex edge-ununfoldable polyhedra, i.e., polyhedra that are combinatorially equivalent to convex polyhedra, yet cannot be cut along their edges and unfolded
Pseudo-Edge Unfoldings of Convex Polyhedra
TLDR
This work constructs a convex polyhedron K in Euclidean 3-space with a pseudo-edge graph with respect to which K is not unfoldable, and confirms that Dürer’s conjecture does not hold for pseudo- edge unfoldings.
arXiv
  • 100 Years of Math Milestones
  • 2019
Edge-Unfolding Nearly Flat Convex Caps
TLDR
A proof that a nearly flat, acutely triangulated convex cap C in R^3 has an edge-unfolding to a non-overlapping polygon in the plane, leading to a polynomial-time algorithm for finding the edge-cuts, at worst O(n^2).
Addendum to: Edge-Unfolding Nearly Flat Convex Caps
This addendum to [O'R17] establishes that a nearly flat acutely triangulated convex cap in the sense of that paper can be edge-unfolded even if closed to a polyhedron by adding the convex polygonal
Affine 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 Durer's
Geometry and Topology
TLDR
This chapter introduces the most important geometrical and topological concepts, considering the two dimensional as well as the three dimensional case, particularly the concepts of the standard ISO 19107 Spatial schema.
Unfolding Prismatoids as Convex Patches: Counterexamples and Positive Results
TLDR
It is shown that the natural extension to a convex patch consisting of a face of a polyhedron and all its incident faces, does not always have a nonoverlapping petal unfolding, however, a positive result is obtained by excluding the problematical patches.
Edge-unfolding nested polyhedral bands
...
1
2
3
...