Their paths crossed in varied ways, with hockey as their common medium. Jeff Sauer coached Brian Rafalski and was mentored by Lou Vairo. Karyn Bye Dietz played for the U.S. women’s team at the 2002 Winter Olympics, winning a silver medal — just as Rafalski did with an American men’s team that counted Vairo among its assistant coaches.

The four were united again Wednesday, when USA Hockey announced they would be inducted into the U.S. Hockey Hall of Fame. Their contributions to the game will be celebrated at a Dec. 4 enshrinement ceremony in the Twin Cities.

Sauer, Bye Dietz, Rafalski and Vairo represent their sport’s growing diversity as well as its traditions. Bye Dietz was on the 1998 U.S. team that won the first Olympic gold medal in women’s hockey and is the third woman elected to the American Hall of Fame as an individual. Sauer, a St. Paul native and longtime coach at Wisconsin and Colorado College, now coaches hearing-impaired and physically disabled athletes at the highest levels.

Rafalski played 11 seasons in the NHL and on three Olympic teams, while Vairo worked with Herb Brooks as a scout for the 1980 Olympic team and assistant coach at the 2002 Winter Games. Though each followed a unique path to the Hall, which is headquartered in Eveleth, all of them shared the same emotions Wednesday.

“My dad said I never had a real job,’’ said Sauer, who coached 11 seasons at Colorado College before a two-decade run at Wisconsin. “To this day, I really have never had a real job. I’ve always enjoyed going to work and being a part of hockey. This is a humbling experience for me.’’

The 1998 women’s Olympic team was inducted into the Hall of Fame in 2009. Captain Cammi Granato, enshrined in 2008, became the first individual woman honored by the Hall; Cindy Curley, a star before women’s hockey joined the Olympics, followed in 2013.

Bye Dietz, an alternate captain for the 1998 Olympic team, led the U.S. with five goals in six games as it won the gold medal in Nagano, Japan. By 2002, when she played in her final Olympics, she had helped spark a women’s hockey revolution.

“It’s incredible how far women’s ice hockey has come,’’ said Bye Dietz, a native of River Falls, Wis., who now lives in Hudson. “It’s been fun to see the growth. Never in my wildest dreams would I predict I’d be sitting here right now being inducted into the U.S. Hockey Hall of Fame.’’

Vairo didn’t play organized hockey while growing up in Brooklyn, N.Y. He recalled skating on a makeshift rink, created by a priest who flooded a schoolyard and hung a string of light bulbs. In 1976, Vairo coached the Austin (Minn.) Mavericks of the U.S. Hockey League to a national championship, and his long career behind the bench included stints as an NHL assistant, with junior and senior national teams and as head coach of the 1984 Olympic team.

Rafalski, a defenseman, played for Sauer at Wisconsin. After being told he was too small to withstand the physical grind of the NHL, he won two Stanley Cups with New Jersey and one with Detroit while amassing 515 points in 11 NHL seasons.

Sauer won two NCAA titles at Wisconsin before beginning his work with disabled athletes. He coached the U.S. to a gold medal at the 2007 Deaflympics, and in what he called the highlight of his career, he led the U.S. sled hockey team to the gold medal at the 2014 Paralympics.