Cool Plane: As a first note, I should point out that the development of aeronef aircraft was bent out of shape on Eliéra because of its lack of fossil fuels – and given the demand for them for lubrication, chemical feedstocks, and so forth, the price of large quantities of them to burn was, ah, not exactly favorable.  Meanwhile, it did possess plentiful radioactive elements, which is one reason why airships were much more popular (and still are for regular passenger/freight transport) in the early days, simply because it’s so much easier to find room for a nuclear steam engine in their mass budget.

But that also meant that when aeronefs were developed apart from the original experimental models and limited-production-run special vehicles, they tended to be in odd areas of the technological envelope by our standards, like nuclear-electric ducted-prop designs, hydrogen-burning turbofans (later propfans), both hydrogen and nuclear thermal (i.e., essentially an air-cooled reactor, Project Pluto-style) ramjets/scramjets, and aerospike rocket engines – sometimes in combination on the same airframe.

As a side note, helicopters are largely excluded from this, because the Empire’s technological development went down a different road to fill their niche.  While the concept does exist in the form of some test models and experimental aircraft, their functional niche is filled instead by tilt-rotors and tilt-turbines.

Some various examples follow:

• The I-2 Starbolt, the first dedicated space interceptor – which is to say, the first plane which was designed to sortie from aerospace cruisers in low orbit rather than from the ground.  It wasn’t the first aircraft to technically be able to achieve low orbit (those aerospikes, don’ch’know?), but it was the first that could repeatably sortie from it, enter the atmosphere, fly a useful mission profile, and return to its mother ship.  Technically, it’s been overtaken by a lot of its successors in the transatmospheric fighter/interceptor and bomber roles both, but the grand old flying-wing that was the first to manage that particular damn cool trick still gets the respect.
  
• While it is a tilt-turbine, and therefore arguably fills the ‘helicopter’ role rather than the ‘plane’ one, the G7-BU Sunhawk is a shameless homage to the A-10 Thunderbolt.  (And one that gets more appreciation than the A-10 does from its own organization, since its particular role is operated organically by the Legions rather than by the Navy, and every legionary knows full well that, in the words of Schlock Mercenary, “When the going gets tough, the tough call for close air support”.)
  
• The K-50C Roustabout cargo plane, the giant dedicated freighter beloved of the Stratarchy of Military Support and Logistics, and by every civilian transport company that’s ever had to face the problem of getting things to places fast on-planet.  It’s a giant, brutish, unbelievably massy monster of an aircraft that flies in the manner of a jet-powered brick, which is to say, by the sheer force of its eight engines.  But it can get more stuff to wherever it’s needed faster than just about anything else in the sky.  If you need, say, an entire prefabricated autofac complex dropped somewhere by the day after tomorrow, you call for these guys.
• The Fireflash 220 semi-ballistic dart is the one commercial plane in the Imperial air fleet whose accommodations are as Spartan as, say, our typical business-class cabin, with added eight-point acceleration harnesses.  That’s because it’s the plane that takes you from one side of the planet to the diametric opposite side in under half an hour, which it does by being closer, in design, to an ICBM than an aircraft.  It takes off and makes a hard burn using its rocket engines, consuming its entire fuel load in just a few minutes.  The engines then cut out, and it goes purely ballistic up into sub-space, then re-enters the atmosphere, aerobrakes, and glides in for a landing on a suitably lengthy runway on the other side of the world no more than 20 minutes later.  (It’s also notorious as the only plane that needs to get landing clearance before it takes off, because once that engine burn happens, it’s committed – it’s either going to land at the place its ballistic course takes it to, or it’s going to crash there.  Most of them do provide a second runway within its extremely limited vector-change capability, but as for diverting to another airport… forget it.  Despite this, though, it has a great safety record.)
  
• At the top end of the flying-wing club, one finds the variations on the theme of the S-1 Rennae superwing – a flying-wing, nuclear-engined aircraft several stories high, the size of a large building.  They can land and take off, but they almost never do unless there’s an emergency; they’re designed for in-flight maintenance, and as long as fuel pellets keep being ferried up to them, they don’t ever really need to land.  They’re mostly used as permanent but mobile airborne installations – the Emergency Management Authority owns a couple to use as mobile disaster headquarters that can orbit the site of the disaster and drop quick-response teams right on top of it, and unlike an airship, can get to it quickly, for example.  Another serves as a flying hotel/cruise liner.