Bodies, over time, break down. But four decades after the NFL’s only undefeated season, the perfect Dolphins lay claim to a legacy that has only strengthened by the year.

Their unequaled excellence, the members of the 1972 Dolphins hold sacrosanct. Some even celebrate with champagne when the last undefeated NFL team of the year falls, preserving their singular history.

Critics have called them petty, but Don Shula — the iconic coach —says that misses the point. It’s simply a source of pride.

“If somebody else does it — we’re not a bunch of angry old guys wishing they get beat — I’ll call that coach and congratulate him,” Shula said.

Until then, the bragging rights are theirs alone. This weekend, when some three-dozen players on the fabled 1972 Dolphins return to South Florida their 40th reunion celebration, the itinerary is loaded.

There will be dinners and parties, a halftime salute Sunday and even the premiere of a new documentary on the team’s impact on Miami.

Defined by perfection, their bond has survived near-tragedies, creaking joints but remarkably few deaths.

Only six have passed since the Dolphins beat the Washington Redskins 14-7 on Jan. 14, 1973, in just the seventh Super Bowl ever played. The most notable death was the beloved Jim “Mad Dog” Mandich, the tight end-turned-radio personality who in April 2011 lost a public battle with cancer. As for those still with us, they are in surprisingly good shape.

Granted, Father Time — and the accumulative trauma from playing professional football — has taken its toll. Defensive lineman Manny Fernandez, now 66, recently had his second back fusion in three months, one of his 15 football-related surgeries.

Earl Morrall, who before he was the mayor of Davie was the Dolphins’ backup quarterback, is just four years younger than his Hall of Fame coach (Shula turns 83 next month). And while his body has noticeably weakened with years, Morrall still insisted on spending the weekend with his old friends.

“Even today, they’re still heckling each other and having fun,” said Nat Moore a former Dolphins player who now oversees their alumni association.

“The fact that [defensive end] Bill Stanfill still likes to get on Earl Morrall about being old, he couldn’t hear and all that. I just think they were a unique group that didn’t have any petty jealousy.”

A unique group, with some unique personalities.

Fullback Larry Csonka is in town from Alaska, where he’s an avid hunter and fisherman, often filming his exploits for cable television. His extreme lifestyle nearly caught up with him in 2005, when his boat capsized during a storm in the chilly Bering Sea. Ten hours later, the Coast Guard was finally able to save Csonka and his crew.

Like Morrall, Dick Anderson went into politics after football. When he wasn’t running several businesses, including the 1972 team’s memorabilia company (in which each player has a share), Anderson got elected to the Florida Senate.

When asked which of his professions was the most cutthroat, Anderson didn’t even pause.

“Politics,” he said. “You can’t trust the people who say something to you.”

Quarterback Bob Griese has been the most ubiquitous of the group, following up his Hall of Fame playing career with a long stint in the broadcast booth. His son, Brian, went into the family business; he was a quarterback in the league for 11 seasons.