Agalmatophilia

Agalmatophilia (from the Greek agalma 'statue', and -philia φιλία = love) is a paraphilia involving sexual attraction to a statue, doll,mannequin or other similar figurative object. The attraction may include a desire for actual sexual contact with the object, a fantasy of having sexual (or non-sexual) encounters with an animate or inanimate instance of the preferred object, the act of watching encounters between such objects, or sexual pleasure gained from thoughts of being transformed or transforming another into the preferred object. Agalmatophilia may also encompass Pygmalionism (from the myth of Pygmalion), which denotes love for an object of one's own creation.
Agalmatophilia became a subject of clinical study with the publication of Richard von Krafft-Ebing's Psychopathia Sexualis. Krafft-Ebing recorded an 1877 case of a gardener falling in love with a statue of the Venus de Milo and being discovered attempting coitus with it.
An important fantasy for some individuals is being transformed into the preferred object (such as a statue) and experiencing an associated state of immobility or paralysis. Such fantasies may be extended to role-playing, and the self-coined term used by fetishists who enjoy being transformed into what appears to be a "rubber doll" or "latex doll".