Think about the aerodynamics of jet plane, a sailboat and a minivan. When we build things to fly through the air or propel us through the water, we design efficient vehicles. Not so with cars.

Aptera, an auto company startup, aims to change that. In just three years, the Carlsbad, Ca.-based firm  has designed and built a remarkably sleek and snazzy three-wheeled, two-seat electric car.

“If a plane looked like an SUV, it wouldn’t take off, “ says entrepreneur Bill Gross, who is a founder and board member of Aptera. “Dophins don’t look like SUVS for a reason. Cars need to look like dolphins, not SUVs.”

Here are a couple of videos showing the car, one from ABC News and another from Popular Mechanics.

The Aptera is “the most aerodynamically efficient vehicle ever,” says Gross. By contrast, according to the company, an average car traveling at 55 mph uses half of its energy just to push air out of the way.

If you pay attention to business, you’ve heard of Bill Gross. He’s a lifelong entrepreneur and the CEO of Idealab, the incubator for new businesses in Pasadena, CA. Bill has birthed spectacular successes and  big flops, among them Knowledge Adventures (educational software, now part of Vivendi), Picasa (photo sharing software, acquired by Google), eToys (an online toy store that overextended itself and failed) and CitySearch (local directories.) Idealab’s GoTo.com introduced the idea of paid search to the Internet, and as such is the underpinning of the $20-billion search market now dominated by Google.

So it’s fitting that Gross is currently doing lots of business with Google. Google is an investor in eSolar, a utility-scale solar thermal power company that recently announced big projects in India and in the Southwest. (You can listen to an interview that I did with Bill Gross about the solar projects and about Aptera at Greenbiz Radio at www.greenbiz.com.) Google has invested in Aptera, too, and it turns out that the company’s beginnings go back to a  Google search.

As Bill tells the story, he was doing some casual research on the Stirling Engine a few years ago when he stumbled across a web page created by Steve Fambro, the founder and now chief technology officer of Aptera. Fambro, an electrical engineer, had posted a design for a vehicle that would be safe, comfortable and fuel-efficient; his initial idea was to make kits so people could build the car themselves. Gross was impressed by the idea of a super-efficient car. “Your dream is my dream,” he recalls saying.“Let’s get together and start a company.” They joined forces with Chris Anthony, who is CEO of a company called Epic Boats (they build wake boats) and an expert in composite materials.

Using computer-assisted design, Aptera’s engineers went on to design a car that weighs just 1,700 pounds with a body made from an impact-resistant material that is lighter than steel but three times as strong.  The car will run 100 miles on a single charge and it’s got some nifty features, including butterfly-styled doors that pop open and a solar-assisted climate control system. Its top speed is 90 mph and it goes from zero to 60 in less than 10 seconds.

“The car is very unusual looking,” Gross says.  “It looks like a futuristic Jetson  vehicle.  But we feel that that’s what it takes to actually make an impact on our energy use and transportation.”

Aptera, which is based in Vista, CA., began taking orders for the cars from California residents at the end of 2007. “Very quickly, we got 4,000 pre-orders,” Gross says. Buyers put down a $500 deposit. The entry-level price for the car is expected to be about $25,000.

Last summer, Google.org announced that it had invested a total of $2.75 million Aptera and a company called ActaCell that makes lithium ion batteries for plug-in hybrids and electric cars. Google didn’t say how much money went into each company but it’s not a lot of dough in any event. Aptera has also raised money from Idealab, Esenjay Petroleum, The Quercus Trust and from Donald R. Beal, the retired chairman and CEO of Rockwell, about $30 million in total. But the company obviously needs a lot more to go into production. Last year, Paul Wilbur, a career automotive executive who worked for 26 years at Ford, Chrysler and a sunroof maker called ASC, was brought in as president and CEO.

Only five of the cars have been built, so far.

Gross tells me he expects to raise the cash in a few months. “Most people would not want to invest in a new car company at a time like this,” he says, “but investors are quite warm to this.” We’ll see.

The U.S. government is a potential source of funding for electric car and battery companies, through the Department of Energy’s advanced technology loan fund. But Aptera has run into a brick wall in Washington. Apparently the government has classified the Aptera’s vehicles as motorcycles, and they aren’t eligible for loans.

I’m delighted that Bill Gross (below) will be at FORTUNE’s Brainstorm Green conference about business and the environment in April, to talk about both eSolar and Aptera. Here’s a chart comparing Aptera’s aerodynamic drag to other vehicles. It’s hard to see, I know, but the company says Aptera is more aerodynamic than a 10-speed bike and 2.86 times more aerodynamic than a Prius.