The crystallographic properties of fluorapatite (FAp) and polytetrafluoroethylene (PTFE) as biomedical materials were compared. Both materials contain fluorine and casually belong to the hexagonal crystal system. It is interesting that FAp is an inorganic ionic crystal, while PTFE is an organic covalent-bond crystal. Generally, fluorine contributes to the physicochemical stability and in some cases to the biocompatibility. The crystal structure of FAp was initially analyzed in 1930 by Naray-Szabo, although the analysis of hydroxyapatite (HAp) was markedly delayed until 1964. The computer graphics display demonstrated that fluoride ions serve to stabilize the hydroxyapatite crystals and prevent dental caries. On the other hand, PTFE crystal analysis was reported in 1954 by Bunn and Howells. The PTFE temperature-pressure phase diagram accepted for over 60 years is very complicated and insufficient. PTFE delicately changes its phase near room temperature, although at a glance it appears to have a simple form compared with DNA.