Lexus LFA

The LFA is one of the strangest cars any mass-market maker has built. Toyota's luxury division spent most of a decade developing it, switching from aluminium to carbon fibre partway through and effectively starting over, to build a hand-made supercar in tiny numbers. It made no commercial sense, and that was rather the point.

At its heart was a 4.8-litre V10 developed with Yamaha, tuned as much for sound as for speed: it spun so fast — past 9,000 rpm — that a conventional analogue tachometer couldn't keep up, so the LFA used a digital one. It produced 553 hp and weighed 1,580 kg, and its engine note is still regarded as one of the finest ever fitted to a road car.

Only 500 were built, across 2011 and 2012. The LFA lost Toyota money on every car — and stands as proof of what the company could do when profit wasn't the brief.