Beverly Hills, Calif. ? “I find sex endlessly interesting,” heiress Gloria Vanderbilt writes in the beginning of her slim new memoir. The rest of the book confirms her fascination with the subject.

“It Seemed Important at the Time: A Romance Memoir” begins with a sexual caper with a girlfriend at school, then journeys to Hollywood, where she was secretly engaged to Van Heflin and dated such luminaries as Frank Sinatra, Marlon Brando, Errol Flynn, Howard Hughes, Bruce Cabot and George Montgomery.

Vanderbilt recalls Sinatra “circling around my secret heart” and revealing his inner soul at midnight suppers, but that much-headlined fling finally ended. So did three of her marriages: to Hollywood agent Pat De Cicco; to the imperious symphony conductor Leopold Stokowski (“Fantasia”), father of her two sons; and to film director Sidney Lumet.

Her only happy marriage was to Southern author Wyatt Cooper, father of two more sons. But he died of a heart attack at 50.

“I’ve had many, many loves,” she remarked in an interview at a Westside hotel. “I always feel that something wonderful is going to happen. And it always does.”

She came here near the end of a six-city book tour.

“When I’m traveling to promote my book, I feel like an artful impostor,” she acknowledged. “What I really am is when I’m in my (painter’s) studio and when I’m writing. With actors, it’s the same thing. They’re kind of artful impostors in public. When you get to know them, they’re different people.”

Gloria Vanderbilt has been in the public eye virtually since she was born into two of America’s most famous old-money families, the Vanderbilts and the Whitneys.

When she was 10, she was portrayed as the poor little rich girl fought over by her aunt and her mother in a sensational custody trial. The aunt won.

Aside from the multiple romances and four marriages, she’s been publicized as an artist (her collages are now on exhibition in New York), sometime actress, author of six books (including three memoirs) and a successful designer of women’s fashions and furniture.

She wears her fame well. She’s open-minded — “I have a tremendous appetite for life; the phone rings and your whole life could change.”

At 80, her green eyes are clear, and her legendary beauty seems little changed. As would be expected, she was dressed in a tastefully elegant style. For the benefit of a fashion-deficient reporter, she described the outfit:

“I’m wearing a Jil Sander jacket, lettuce green and lavender tweed with metallic threads, black Jil Sander pants and a black camisole. And a gold necklace that Sinatra gave me; I wear it for luck when I travel.”

Vanderbilt’s father died when she was 15 months old, and she was brought up “surrounded by women.”

“If you don’t have a father, you don’t miss it, because you don’t know what it is,” she said. “It was really only when I married Wyatt Cooper that I understood what it was like to have a father, because he was just an extraordinary father.”

One of their sons is CNN news anchor Anderson Cooper, who has said he considers his mother’s memoir “a terrific book; it’s like an older ‘Sex and the City.'”

Vanderbilt lives in a Manhattan apartment and does her artwork in a studio on the floor below “so I can work day and night.”

And she apparently hasn’t abandoned her pursuit of love. Toward the end of “It Seemed Important at the Time,” she writes of a mystery man who lives in Chicago.

She lists a dozen of his failings, and yet he apparently has a method of lovemaking that keeps drawing her back to Chicago.

“What more can a girl want?” she concludes. “We can’t have everything — but oh, we can try — we can try.”