The crystal structure of polytetrafluoroethylene, -(CF2)(n)-, is unusual in having a number of crystal forms and also possessing substantial molecular motion within the crystal well below the melting point. This article deals with the unusual first-order transition occurring at about 19 degrees C, changing the crystal structure from form II to form I. This article also updates current literature on the crystal structures of these two forms. X-ray and electron diffraction data from forms II and IV are interpreted as helical structures. Form LI is defined mathematically as a non-commensurable helix close to a 13/6 conformation of six turns per 13 (CF2) groups. Form IV is interpreted as a commensurable 15/7 helix which is consistent with space group P3(1). Fiber diffraction patterns of these forms are described in detail.