This principal runs a school of “no.”

Students at PS 106 in Far Rockaway, Queens, have gotten no math or reading and writing books for the rigorous Common Core curriculum, whistleblowers say.

The 234 kids get no gym or art classes. Instead, they watch movies every day.

“The kids have seen more movies than Siskel and Ebert,” a source said.

The school nurse has no office equipped with a sink, refrigerator or cot.

The library is a mess: “Nothing’s in order,” said a source. “It’s a junk room.”

No substitutes are hired when a teacher is absent — students are divvied up among other classes.

A classroom that includes learning-disabled kids doesn’t have the required special-ed co-teacher.

About 40 kindergartners have no room in the three-story brick building. They sit all day in dilapidated trailers that reek of “animal urine,” a parent said; rats and squirrels noisily scamper in the walls and ceiling.

And the principal — Marcella Sills, who joined PS 106 nine years ago — is a frequent no-show, sources say.

Sills did not come to school last Monday. On Tuesday, she showed up at 3:30 p.m.

On Wednesday, The Post found her at home in Westbury, LI, all day before emerging at 2:50 p.m. — school dismissal time. Wearing a fur coat, she took her BMW for a spin.

She showed up at school Thursday, but not Friday.

When Sills, 48, does go to work, it’s rarely before 11 a.m. — and often hours later, say sources familiar with her schedule.

“She strolls in whenever she wants,” one said.

The school hasn’t had a payroll secretary in years.

A Department of Education spokesman said Sills was required to report her absences and tardiness to District 27 Superintendent Michelle Lloyd-Bey but would not say whether Sills did so last week.

Lloyd-Bey did not return a call. Sills hung up on a reporter.

When she is out, an assistant principal is left in charge. Yet Sills, who gets a $128,207 salary, also pockets overtime pay — $2,900 for 83 hours in 2011, the latest available records show.

“This school is a complete s- -thole, but nobody in a position of power comes to investigate. No one cares,” a community member said.

PS 106 families hope their cries for attention bring newly installed Schools Chancellor Carmen Fariña to the rescue, saying they can’t recall any prior DOE leader visiting the remote school.

She would find it sinking, they say.

The isolated building sits a block and a half from the beach, surrounded by vacant, weed-choked lots, the road behind it strewn with trash bags and broken TVs.

The floods of Hurricane Sandy in October 2012 wrecked a hangar-like annex, called the Early Childhood Academy, which housed pre-K, kindergarten and first and second grades. It has not been repaired.

Two kindergarten classes moved into “temporary classroom units” in the yard. The other children moved into the main building, forcing some classes to squeeze into small offices and storage rooms. The pre-K class sits in the auditorium, but has to move to the cafeteria during the movies.

Kids in several grades said that last week they watched “Fat Albert,” “Alvin and the Chipmunks” and “Monsters, Inc.,” but did not relish the downtime.

“I like gym. I like to draw,” said Charm Russell, 10, who added her peers are too restless and bored to watch the screen. “They’re always making noise, and there’s nothing entertaining going on. No art, no gym, no music class.”

More alarming, the teachers have gotten no curricula since Sandy. Last February, the DOE announced several new options, including “Go Math” for grades K-5, and “ReadyGen” or the state Education Department’s “Core Knowledge” for English language arts. The books cover the Common Core standards, skills that kids should master at each level.

But five months into the school year, PS 106 classes still don’t have the books or teacher’s guides.

“They have no reading program, no math program,” a source said, adding Sills blames outside administrators for not sending materials.

Teachers muddle through by printing out worksheets they find online, buying their own copy paper.

The DOE gave no explanation for the missing curricula but said it’s “working with the school to provide students with physical education.”

A spokesman denied the trailers are rat-infested.

Staffers won’t speak up or even file a grievance with their union because Sills will retaliate, a source said.

Parents wonder if higher-ups know what’s going on.

“Why don’t they get on them? I don’t understand that,” said Michael Moore, father of a second-grader.

Another father, Roland Legions, added. “They’re not doing right by the kids.”

One mom said she couldn’t get a meeting with Sills to discuss concerns. Another said Sills is “just not professional.”

“She should be here,” the mom said. “How is she going to run the school if she’s not here?”

PS 106 is allocated $2.9 million to serve a low-income population with 98 percent of its students eligible for free lunches. As a Title 1 school, it gets extra federal funds, but community members say they’ve never seen a budget tracking the income and spending.