An Algorithm for Folding a Conway Tile into an Isotetrahedron or a Rectangle Dihedron

Abstract

Every net of an isotetrahedron (I) or a rectangle dihedron (RD) is a Conway tile. Reversely, it is shown by using Alexandrov's theorem that every Conway tile can be folded into either I or RD. However, it was not known how to fold a given Conway tile into I or RD. The purpose of this paper is to give an algorithm for folding a Conway tile into I or RD. Moreover, for a given Conway tile we present a method to identify the exact shape of I or RD into which it can be folded.