Objectum sexuality.

Objectum sexuality is characterized by a strong romantic and sexual attraction to inanimate objects. Objectum sexuals develop relationships with the objects that they love.

The best known objectum sexual is a woman named Erika Eiffel. She's appeared on several American talk-shows, and is the central character in the documentary Married to the Eiffel Tower (it looks like it's a dead link, but click play):

An observation documentary about women who fall in love with large objects rather than people. They maintain to have intimate relationships with them, including comunicating with them through telepathy.

Vice published a piece early last year discussing objectum sexuality that describes the struggles and judgment that Erika Eiffel has experienced. It also discussed the nature of objectum sexuality.

From Vice:

Breaking Up with the Eiffel Tower: Heartbreak Is No Less Real for Objectum Sexuals
By Nell Frizzell
Loss, grief, heartache: Breakups are no less painful when you're doing it with a bridge. Or a pylon. Or a wooden fence. Or the Eiffel Tower.
So argues Erika Eiffel, the tower crane operator and former award-winning archer made famous by the documentary Married to the Eiffel Tower. Erika is one of the few public objectum sexuals—people with a love orientation toward objects—and, in addition to holding a commitment ceremony with the 186-year-old French iron tower, has fallen for fighter jets, fencing, and is currently in a relationship with a crane. She also runs the support website Object Sexuality Internationale.
We don't know how many objectum sexuals there are in the world—not enough data has been gathered and people are, understandably, reluctant to identify their orientation in such a climate of distrust and misinformation. We do, however, know that objectum sexuality is found in both men and women across the world. In 2010, the clinical sexologist Dr. Amy Marsh wrote in the Electronic Journal of Human Sexuality that, while it is often assumed that OS is "a pathology" or related to "a history of sexual trauma," there is, in fact, no data to support such a claim and that "OS appears to be a genuine—though rare—sexual orientation."

Read the rest here: link.