Paper by Erik D. Demaine

Reference:

Vincent Bian, Erik D. Demaine, and Rachana Madhukara, “Edge-Unfolding Prismatoids: Tall or Rectangular Base”, in Proceedings of the 33rd Canadian Conference in Computational Geometry (CCCG 2021), Halifax, Nova Scotia, Canada, August 10–12, 2021, pages 343–347.

BibTeX

@InProceedings{Prismatoids_CCCG2021,
  AUTHOR        = {Vincent Bian and Erik D. Demaine and Rachana Madhukara},
  TITLE         = {Edge-Unfolding Prismatoids: Tall or Rectangular Base},
  BOOKTITLE     = {Proceedings of the 33rd Canadian Conference in Computational Geometry (CCCG 2021)},
  bookurl       = {https://projects.cs.dal.ca/cccg2021/},
  ADDRESS       = {Halifax, Nova Scotia, Canada},
  MONTH         = {August 10--12},
  YEAR          = 2021,
  PAGES         = {343--347},

  withstudent   = 1,
  unrefereed    = 1,
  dblp          = {https://dblp.org/rec/conf/cccg/BianDM21},
  comments      = {This paper is also available from the <A HREF="https://projects.cs.dal.ca/cccg2021/wordpress/wp-content/uploads/2021/08/CCCG2021.pdf#page=353">electronic proceedings</A> and as <A HREF="https://arXiv.org/abs/2106.14262">arXiv:2106.14262</A>.},
}

Abstract:

We show how to edge-unfold a new class of convex polyhedra, specifically a new class of prismatoids (the convex hull of two parallel convex polygons, called the top and base), by constructing a nonoverlapping “petal unfolding” in two new cases: (1) when the top and base are sufficiently far from each other; and (2) when the base is a rectangle and all other faces are nonobtuse triangles. The latter result extends a previous result by O'Rourke that the petal unfolding of a prismatoid avoids overlap when the base is a triangle (possibly obtuse) and all other faces are nonobtuse triangles. We also illustrate the difficulty of extending this result to a general quadrilateral base by giving a counterexample to our technique.

Comments:

This paper is also available from the electronic proceedings and as arXiv:2106.14262.

Availability:

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