Flat 2-Foldings of Convex Polygons
A folding of a simple polygon into a convex polyhedron is accomplished by glueing portions of the perimeter of the polygon together to form a polyhedron. A polygon Q is a flat n -folding of a polygon P if P can be folded to exactly cover the surface of Qn times, with no part of the surface of P left...
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| Main Authors: | , , , |
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| Format: | text |
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Archīum Ateneo
2005
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| Subjects: | |
| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/81 https://link.springer.com/chapter/10.1007%2F978-3-540-30540-8_2 |
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| Institution: | Ateneo De Manila University |
| Summary: | A folding of a simple polygon into a convex polyhedron is accomplished by glueing portions of the perimeter of the polygon together to form a polyhedron. A polygon Q is a flat n -folding of a polygon P if P can be folded to exactly cover the surface of Qn times, with no part of the surface of P left over. In this paper we focus on a specific type of flat 2-foldings, flat 2-foldings that wrapQ ; that is, foldings of P that cover both sides of Q exactly once. We determine, for any n, all the possible flat 2-foldings of a regular n-gon. We finish our paper studying the set of polygons that are flat 2-foldable to regular polygons. |
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