Flat 2-Foldings of Convex Polygons

• Main Authors: Akiyama, Jin, Hirata, Koichi, Ruiz, Mari-Jo P, Urrutia, Jorge
• Format: text
• Published: Archīum Ateneo 2005
• Subjects: Singular Point; Interior Point; Equilateral Triangle; Convex Polygon; Convex Polyhedron; Geometry and Topology; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/81; https://link.springer.com/chapter/10.1007%2F978-3-540-30540-8_2
• Institution: Ateneo De Manila University

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.