This is rich!

The poor will use a separate door under plans for a new Upper West Side luxury tower — where affordable housing will be segregated from ritzy waterfront condos despite being in the same building.

Manhattan developer Extell is seeking millions in air rights and tax breaks for building 55 low-income units at 40 Riverside Boulevard, but the company is sequestering the cash-poor tenants who make the lucrative incentives possible.

Five floors of affordable housing will face away from the Hudson River and have a separate entrance, elevator and maintenance company, while 219 market-rate condominiums will overlook the waterfront.

“You know that show ‘Downton Abbey’? Where the servants have to come and go through separate entrances and bow their heads when they see a noble?” wrote the author behind the blog West Side Rag. “Well, there could soon be a version right here on the Upper West Side!”

Extell broke ground on the building between West 61st and West 62nd streets last year as part of the 15-tower Riverside South residential complex stretching to West 72nd Street.

Now the company is applying for the city’s Inclusionary Housing Program, which gives developers more floor area in exchange for building on- or off-site affordable housing.

But instead of building a larger condo, Extell plans to sell the bonus floor area to another building within a half-mile of the site. Real-estate attorneys say such a sale could be worth millions.

Extell is also seeking a controversial 421a exemption — a tax break given to developers who include affordable housing in their market-rate buildings.

In October, The Post reported that five of the luxury firm’s towers cost the city $21.8 million in tax revenue in their first year alone.

Together, the buildings paid just $567,337 in annual taxes. Without the 421a program, they would have paid the city $22 million, according to appraisal firm Miller Samuel Inc.

Extell declined to comment.

A spokesman for the Department of Housing Preservation and Development said Extell’s application is still under review.

Assemblywoman Linda Rosenthal, a Democrat who represents the Upper West Side, told The Post that Extell’s plans “smack of classism,” and feared they could set a dangerous precedent for other developers.

“It’s a blatant attempt to segregate people,” fumed Rosenthal, who is demanding that HPD deny Extell’s request for tax breaks. “It’s just not a good thing for the city of New York to be supporting.”“I hate the visual of market-rate tenants going in one door and affordable tenants going in another, but that’s a visceral reaction,” Diller said.

Community Board Chair Mark Diller sent a letter to HPD last month asking for safeguards to protect low-income residents, who are relegated to floors two to six.

Under Extell’s plans for the low-income units, a studio will go for $845 a month, a one-bedroom for $908, and two-bedrooms for $1,099.

Households with incomes below 60 percent of the city’s area median income qualify for the units.

A family of four, for example, would need to make less than $51,540; an individual would need to earn less than $36,120.

Fat cats living in the condos will pay more than $1,000 per square foot. At The Aldyn, Extell’s 40-story luxury building next door, one-bedrooms sell for a whopping $1.3 million. A six-bedroom, eight-bath pad goes for $15.9 million.