It is a five-door, all-wheel-drive hatchback with the sporting looks of a luxury coupe. It is as close as you can get to the motorized equivalent of having your cake and eating it, too — performance in passionate conjugation with utility, high style in elopement with practicality. And it even has the nerve to flirt with fuel economy!

Not long ago, a car such as the 2012 Audi A7 3.0 TFSI, the subject of this week’s column, would have been considered a crazy idea. Sensible executives would have stamped it an undoable business proposition. Many consumers, more interested in performance and prestige than common sense, would have looked askance at the more pedestrian aspects of its design intent. In a global sales environment unburdened by green environmental concerns, the timing was all wrong for a car of its type.

But circumstances have changed. The availability of oil is no longer a sure thing. And even if oil’s presence were eternally guaranteed in ample amounts, there are serious questions about Earth’s ability to support the continued use of fossil fuels without fatally poisoning the planet’s air and water. And because of the recent failures of economies worldwide, prestige without portfolio — luxury absent any useful value — is fast becoming a thing of past pretensions.

Automobile manufacturers nowadays are scrambling to develop products that comply with changing externalities affecting their businesses. It is a difficult mission, especially at the luxury end of the market, where success historically has been measured by the appeal of the exceptional — most often, the exceptionally unnecessary, desirability stemming solely from exclusivity.

Audi has developed a car to deal with that marketing conundrum, the 2012 A7 TFSI — the letters referring to an engine technology that combines fuel injection (what Audi calls “fuel stratified Injection) with “supercharging,” a method of pulling more air into engine combustion chambers for a cleaner, more complete burn of the air-fuel mixture.

In the A7, that means more power out of a smaller engine with no appreciable increase in fuel consumption. Think of it as getting V-8 horsepower out of a V-6 engine without the weight or the fuel penalty of a V-8. The reality in the A7 is a 3-liter, supercharged V-6 with direct injection and variable valve timing (310 horsepower, 325 foot-pounds of torque) that moves the car from 0 to 60 miles per hour in 5.4 seconds.

Most of us don’t waste time or fuel launching ourselves from “stop” (fast starts are almost always more fuel-consumptive). But rare is the motorist among us who does not appreciate steady, reliable torque — authoritative at low speeds, masterful at crescendo on highway runs. The feeling is absolutely sensual, addictive. I found myself hunting for empty Virginia roads in the wee morning hours just to enjoy that feeling over and over again.

That’s the silly, impractical part of the A7 — performance much in keeping with its mind-bending visual appeal. True story: On two occasions, I put the A7 in restaurant parking lots only to lose it after dining. Why? I left the A7 thinking that I had parked an exotic coupe. Instead, I had parked a five-door hatchback, the most practical of practical family sedan designs.

When I finally stumbled upon the A7, I was confused. It certainly looked like a hot coupe. But it had four side doors and a long rear hatch. Audi’s designers used three prominent lines — upper, middle, lower — to conceal the A7’s homely design origins. The lines, in conjunction with a rear quarter that looked more “coupe” than most coupes, give the A7 an air of muscular sensuality.

Inside is all of the stuff that traditionally defines automotive luxury as luxury — in this case, dark walnut inlays on the instrument and door panels; supple, yet anatomically contoured Valcona leather seating surfaces; every conceivable electronic infotainment device or access portal. It is all put together perfectly in a cabin so quiet, it bestows solitude upon entry.

But if life takes a turn toward the sweaty practical, the A7 (I drove the Prestige version for this report) can handle that, too. Lift the rear hatch. With all four sets in place, you have 24.5 cubic feet of storage space. Lower the rear seat backs, and you nearly double your cargo room.

The surprising thing is that the A7 does not act the wimp under load — no groaning, tail-wagging, or slouching about.

Finally, there is the matter of the A7’s all-wheel-drive system, which provides a 40-60, front-rear power split under normal driving conditions but constantly and rapidly varies that application of drive power on an as-needed basis in inclement weather. All it takes is one severe rainstorm, such as the one I ran into near Manassas, to fall deeply, madly in love with Audi’s all-wheel-drive system. I was thus smitten.