Foldings of regular polygons to convex polyhedra I: Equilateral triangles

Abstract

To fold a regular n-gon into a convex polyhedron is to form the polyhedron by gluing portions of the perimeter of the n-gon together, i.e. the n-gon is a net of the polyhedron. In this paper we identify all convex polyhedra which are foldable from an equilateral triangle. © Springer-Verlag Berlin Heidelberg 2005.