FRANKFURT (Reuters) -

What price exclusivity? If you ask Lamborghini, one million euros ($1.4 million) should do it -- before tax, of course.

In a bid to add more prestige to what it already has, the Italian maker of super luxury sports car unveiled the Reventon at Frankfurt's international autoshow, a very limited edition car that looks more like an arrow than anything on four wheels.

With the six-figure price tag, it is the most expensive car that it has ever built.

Needless to say, Lamborghini has already sold the 20 cars that it plans to build.

"As soon as the word got out, we sold out in four days," Chief Executive Stephan Winkelmann told Reuters, adding that they could have easily sold another 20.

Most of the buyers were men from the United States, Lamborghini's biggest market, he said.  Some of them are already owners of a Lamborghini, which competes with the likes of Ferrari in speed and exclusivity.

"We have among our customers movie stars, sports stars... (but) the majority of our clients are businessmen. Men. Lovers of luxury goods," said Winkelmann.

True to its tradition of cultivating an aggressive image, Lamborghini named the car after a bull that killed matador Felix Guzman in 1943.

Although it is based on its Murcielago LP640 model, Lamborghini's engineers took inspiration from a fighter jet and reworked the composite carbon fiber body to accentuate the sleekness and angular edges usually associated with its cars.

The engine is the same as the LP640: a 12-cylinder rocket that can propel the car from zero to 100 km/h in 3.4 seconds.

By comparison, the coupe version of the LP640 costs a relatively more modest 219,600 euros.

Lamborghini, which is run by Volkswagen's (VOWG.DE) Audi division, will start making the Reventon in January and deliver them in October.

The car, which came in an opaque grey at the autoshow, has a three-year warranty.