After the Giants’ three World Series runs and the subsequent media exposure, the humongous glove behind the AT&T Park bleachers might be the sports world’s best-known sculpture of an object.

As such, a legend has evolved that the model was a glove owned by the father of Giants executive Jack Bair. But that’s not how Ron Holthuysen remembers it — and he’s the guy who built the monument.

“I am from Holland,” he said, “so I know nothing about baseball.”

That turned out to be an advantage, because when he was asked to put a baseball glove in the scale model for a plaza to surround the big Coca-Cola bottle at what was to be known as Pac Bell Park, he didn’t know old from new. So he went to Urban Ore, a thrift store near his Berkeley home, and asked whether they had any baseball gear.

The clerk brought out a box of old gloves. “This model was, for me, the most sculpturally interesting, so we made a mold of it and put it in the presentation model, and everybody loved that mitt,” he said, still unaware of the difference between a mitt and a glove.

A glove has fingers and “mitt” is short for mitten. The glove at AT&T only has three fingers plus a thumb, the way they were made in the 1920s. The glove that belongs to Bair is from the 1940s, with four fingers plus a thumb.

“Jack Bair’s father’s mitt has five fingers,” said Holthuysen, who said the Bair glove may have inspired the idea of a glove-sculpture at the park, but it had nothing to do with the glove that was sculpted.

Bair’s original idea was for the Coke bottle to pour into a dunk tank. But when Coca-Cola executives balked at that, he dashed to his office and returned with his father’s glove.

From that point, Bair, senior vice president and general counsel for the Giants, stands by his story. Here’s how he tells it to The Chronicle:

“In a planning meeting for the new ballpark, the design team working on the Coca-Cola attraction was brainstorming with us about what artistically should go with the bottle.

“I pitched an idea of a dunk tank in the form of a classic Coca-Cola contoured glass (the person would be dunked when the Giants scored, much like Bernie Brewer slides into a beer mug when the Milwaukee Brewers score).

“They wanted something more classic baseball. I had my father’s old glove on display in my office, retrieved it during the discussion and brought it to the meeting. They loved it, asked to borrow it and had it digitally scanned and reproduced it on the larger scale. They modified it slightly, but if you look at the original in my office and the actual Giant glove, they look almost identical in all other respects than the loss of one finger!”

Whatever the case, the lore of the glove doesn’t stop there. A rumor has been swirling that women’s underthings were hidden in the layers of fiberglass and epoxy, as it was being constructed by Scientific Art Studio.

According to Holthuysen, that report is true.

“The team that worked on it were eight or nine women,” Holthuysen said, “and when they were done they thought it would be funny to put their bras in it.”

Holthuysen and his team at Scientific Art Studio in Richmond have built 60 life-size or larger animal sculptures for display at the San Francisco Zoo. That raises the question: What mementos will they leave there?

“Maybe something in the whale,” Holthuysen said.

Sam Whiting is a San Francisco Chronicle staff writer. E-mail: swhiting@sfchronicle.com Twitter: @samwhitingsf