Perched high in the exclusive Southridge community, with panoramic views of the Coachella Valley, including the city of Palm Springs and the San Jacinto Mountains, the 23,366-square-foot home was designed in 1973 by the California Modernist architect John Lautner. It was built to resemble a volcano, with three visorlike arches and an undulating concrete roof, a hole at its center opening a courtyard to the sky. The roofline has been described as one of the most distinctive works of architecture in the Coachella Valley. The house has also been likened to a giant mushroom. Its original wood frame burned down during construction, in a fire sparked by a welder. Work was finally completed in 1980.

Used mostly as a second home and entertaining space by the Hope family, it can accommodate as many as 300 guests for dinner under an enormous covered terrace. Each January for many years, the family threw a huge dinner party to mark the end of the Bob Hope Classic golf tournament, now called the Humana Challenge. “That was sort of a highlight of the desert social calendar,” said Linda Hope, a daughter of the couple.

Mr. Hope died in 2003 at the age of 100; Mrs. Hope died in 2011 at 102. “Mother and Dad would sing together,” Ms. Hope said.

Tony Bennett, Glen Campbell and film starlets would visit the home. A big buffet would be laid out on the terraced patio, including Mrs. Hope’s famous antipasto salad, which she insisted on mixing herself, adding the vinegar and oil by eye. A clear tent was put up on part of the terrace to keep out the cold while still allowing guests to take in the spectacular nighttime view. “The whole desert was at your feet,” Linda Hope said.

The home, which is being listed with Ann Eysenring, a broker with Partners Trust Real Estate of Beverly Hills, and Patrick Jordan and Stewart Smith of Windermere Real Estate in Palm Springs, has 6 bedrooms, 10 bathrooms, 3 half baths, indoor and outdoor pools, a pond, putting greens and a tennis court.

Mr. Lautner, the architect, eventually distanced himself from the project after Mrs. Hope hired a designer to make changes to the interior. None of them constituted a major alteration of the Lautner design, which includes a boulder jutting into the living room; she simply made interior modifications to make it “more livable,” according to Linda Hope. The changes included extending the dining room toward a balcony and making it possible to get from the bedrooms to the front door without crossing a patio, Ms. Hope said.

“I think my mother was a frustrated architect,” she added, noting Mrs. Hope’s serial remodeling of their primary home in Toluca Lake, Calif. “My dad used to say every time he went away he needed a road map to get back through his house.”

In Palm Springs, Mrs. Hope commissioned the artist Garth Benton, who painted the murals on the garden walls at the Getty Villa educational center and museum in Malibu, to paint a Rousseau-like mural on the back wall of the bar, and a lush, greenhouse-like wall of plants in the spa, which houses a pool, a hot tub and an exercise area.

It was Mrs. Hope who spent the most time at the Palm Springs house, while her husband traveled extensively, and famously, for work. Each November, Mrs. Hope would travel from Toluca Lake with a caravan of cars to carry the clothes, dishes and silverware she thought she would need for the season. “People used to laugh and say, the court is moving,” Linda Hope joked, adding: “She absolutely adored the place. My dad did, too.” But it wasn’t until her parents were in their late 80s and 90s, she said, that they really spent more time there together.

Bob and Dolores Hope, who were avid golfers, loved the desert, Ms. Hope said. The Lautner-designed house was their third home in Palm Springs and their “dream house.”