Agalmatophilia is the sexual attraction to a statue, doll or mannequin. Pygmalionism, refers to a state of love for an object of one's own creation, but may also be used to describe the attraction to statues.
Preferences in the individual
Agalmatophilia also crosses over into transformation fetishism in the form of fantasies about people transformed into any of those objects. For many it is the idea of immobility or loss of control that is arousing rather than an immobile object per se, and so there are also fantasies about mannequin-like paralysis which sometimes cross over into hypnofetishism and robot fetishism.
Such fantasies may of course be extended to roleplaying, and the self-coined term used by fetishists who enjoy being transformed appears to be "rubber doll" or "latex doll".
Representation in the arts
A number of famous art photographers have extensively featured sexualised life-sized dolls in their work, such as: Hans Bellmer, Bernard Faucon, Helmut Newton, Morton Bartlett, Katan Amano, Kishin Shinoyama, and Ryoichi Yoshida.
Agalmatophilia features prominently in Tarsem Singh's 2000 thriller movie The Cell. The movie centres on a serial killer named Carl Stargher who drowns his victims (all young women) and then bleaches their bodies so they resemble dolls. He then masturbates while hanging himself above them.
Later on in the movie there is a scene taking place inside his mind in which a psychiatrist finds a collection of grotesque, doll-like, corpse-like women inside display cases depicting scenes, while attached to crude machinery that jerks them about in sadomasochistic sexual poses; how the killer percieves his victims.