The Littleton Coin Co. of Littleton, N.H., has done a great service, offering 2012 presidential dollars that feature three of the more obscure leaders who just happened to sport some of the most interesting chief-executive facial hair: Chester A. Arthur, Grover Cleveland, Benjamin Harrison and Grover Cleveland again, from his second, nonconsecutive term.

But presidential-history nuts should act fast because these coins “will never be minted again,” a Littleton Coin ad declares.

The ad, with the leaders’ visages in gold splendor, sent us tumbling down a presidential rabbit hole.

What if the coins are these presidents’ last, best chance at being remembered?

Is the Arthur coin his only legacy?

Is their relative anonymity the fault of fate or of something more nefarious?

“Maybe these individuals are ignored because of their facial hair,” said Jonathan Sessions, founder and treasurer of the recently launched BEARD PAC. After all, he continued, “Benjamin Harrison was the last president that had a full beard.”

Sessions doesn’t completely buy the premise that the men have left behind no legacy. Cleveland, after all, has the distinction of having been our nation’s 22nd and 24th president. And Harrison was behind the Sherman Anti-Trust Act, which, according to Sessions, “is an absolutely important piece of legislation.”

Sessions traces his knowledge of U.S. presidents to a former pastime: biking. (He memorized trivia on long rides.)

Still, even he has trouble recalling memorable bearded presidents. Except for one.

“Obviously [President] Abraham Lincoln had a beard,” he said. “But perhaps [that’s because] he was involved in a difficult period for this country.”

Maybe …

Aaron Perlut, chairman of the American Mustache Institute, was deeply troubled by the fact that Arthur, Cleveland and Harrison have been overlooked.

“When people wax poetic on leaders, it’s commonly lost on mortal Americans that Chester A. Arthur was the greatest president of the United States, ever,” Perlut said. “And it’s so sad that only now, 128 years after his death, Arthur’s rugged good looks are emblazoned on a U.S. Mint-issued coin.”

Arthur’s greatest achievement is obviously “his magnanimous lip forestry,” though Perlut did tell HOH about his support for the Pendleton Civil Service Reform Act, a nail in the coffin of government nepotism.

Meanwhile, people should get these coins while they’re hot, because Littleton says they won’t be around forever.

“The coins have a limited run,” Jill Kimball, spokeswomen for the Littleton Coin Co., patiently explained to HOH. “So, say they had a print run of 2 million, so that’s what is produced.”