Difficult to find decent pictures of this one : Prost AP05 that was meant to race in 2002
If they'd had the money in late 01, AFAIK, the car Phoenix racing showed up with (but never was allowed to enter with) was AP04B(AP04 with the rear of the Arrows 3-seater!!). If Prost and Diniz could've come to an agreement the car might've been built as well, as the DGP01, Diniz Grand Prix. There is tonnes of stories like that in F1. E.g did you know that "German Grand Prix Racing" tried to buy Arrows in 02? They even got 60% of the shares of the team in October 02, and filed an entry for 2003. But Arrows had legal issues. German Grand Prix Racing never paid of Arrows debts, and they pulled out.
Just to try to enter in 2004, now with customer cars from Jaguar, Craig Pollock as team boss. They even signed two German drivers to be test-drivers. It was said that Eddie Irvine would be one driver, and either Verstappen or Sarah Fisher(!) the second. They even said they had sponsors signed.
In the end, Ford (Jaguar) only got one cheque, which wasn't collectible.
So, then they moved over to Minardi, who always needed money. They had one meeting with Paul Stoddard, after which Stoddard considered it too be too good to be true, and never had another meeting. A short time after, there was an accusement of fraud from prosecutors in Germany, and like Bernie Ecclestone said "He is a fine guy who always forgets to pay". And that was the end of the "German Grand Prix Racing" story.
Anyway, this was about pictures, right?
I guess the Caterham CT07 is well known
Probably also the Epsilon Euskadi one (they tried to enter in 2010 and 2011, cannot remember why they wasn't chosen for 2010, but the FIA decided to not let anyone enter in 2011)
However, the Arrows AMT 21 is a bit more rare. And in the end, AMT->Asiatech and the Arrows A22 was with Asiatech engines.
The DAMS GD01 was never raced. It was tested though. Gerard Larousse wanted to use this car for his Larousse team in 95, as DAMS wasn't in a hurry to enter F1, and Larousse didn't have money to make his own. That didn't happen. DAMS tested a bit in 95, but with the 107% rule being added to F1 in 96, and the fall of Simtek and Pacific, DAMS decided to not enter F1, as they knew that car was very conservative and needed race mileage to develop. The Xtrac designed gearbox would go on to another never-raced F1 car.
Namely the Dome F105. The car was tested during the 96 season, but lack of funding prevented them to open an European base. However, Marco Apicella (shortest F1 race career in history), Naoki Hattori and Shinji Nakano did get to test the car in Japan. They did a test at Suzuka right after the Japanese GP in 96. Being 0.3 sec off the 107%. And they stopped. It was an attempt to get funding later on, by Prince Malik, who later "invested" in Arrows (anyone remember t-minus on the 99 Arrows?), nothing came from it. The car is stored at the Dome HQ today.
The Brabham B58Y was the Yamaha-test mule, that convinced Brabham to go with Yamaha engines a year later. However, the car was never raced as they had a race deal with Judd.
AGS one of many teams that struggled in the late 80's early 90's in F1. They raced a JH25B and JH27 car, but never the JH26. It was said that the JH27 was nothing more than a JH25B with random parts swapped, in an effort to pretend it was a new car and secure sponsorship. The JH26 however, never saw the light of day! With that being said, this car looks surprisingly good for a 1991 design, raised nose and all.
Lastly, in reality OT, as it was only drawings. The Ikuzawa drawing from 93/94. The team had employed Peter Windsor, Enrique Scalabroni who was well known for having worked as a designer for Williams and Ferrari in the 80 and early 90's, Peugeots Le Mans winner in 92 and the Peugeot F1 car. Probably most famed for having designed the "Cross F1 car". With one front-wheel in the middle, one rear-wheel at the rear, and two wheels on the side of the car, at the mid-point. Anyway, Ikuzawa made a full scale mock-up of the car, John Watson did seat-fitting. The plan was to have Kenny Bräck and Gil de Ferran as drivers. Windtunnel results were very promising, sponsors lining up. And they were in extensive talks with Ford and Cosworth.
Then came the Japanese economic slump in the mid-90's and the team hit trouble. Without being able to seal a deal with Cosworth, the majority of the employees left to Stewart Grand Prix, and the Ikuzawa was halted. Rumours were that Stewart would buy the HW001 design, but they denied it. Regardless, with the team almost entirely made up by Ikuzawa staff, there is no doubt that they brought their knowledge of the HW001 to Stewart when working on the Stewart GP's first car.
As Peter Windsor later said. "Another factor that hurt us a little was the Ford engine contract going to Jackie Stewart. He deserved it, of course, but we were talking extensively to Ford and Cosworth back in 1994-95".
As you might tell. I am quite a bit of a fan of the more obscure things in F1. Backmarkers, strugglers, dreamers.