From what I know about engines (not much!) they take some time to start (crank). How does the Prius achieve almost instant starting of the engine, sometimes many times per minute? Also, I thought that engines are wasteful of fuel and battery power during the startup crank.
Only when they're cold, really. When they're already warm and optimally repositioned for fairly instant light-off [as the hybrid controller indeed does with the ICE as it's brought to a standstill], there's no appreciable overhead in a restart. There's a short burst of battery current to spin it, injection begins, and off you go. . _H*
A regular gasoline engine uses a small electric motor to start the engine. The motor can rotate the engine at only around 300 rpm or so. That small starter motor makes plenty of noise so it is obvious when it is running. Prius uses one of two motor generators located in the transaxle to start the gasoline engine. The motor generator can produce much greater power and torque (compared to the little electric motor used as a starter motor in regular cars) and will spin the gasoline engine at ~1,000 rpm. Further, the motor generator does not make much noise, so it is not always obvious when the gasoline engine starts.
Further, the motor generator is always "engaged" with the engine. So you don't have a solenoid to fire. There are no gears to shift around. The Prius uses "magnetics" to engage/disengage various "power paths" in the HSD. This is also how the "CVT" works, though personally I don't like the use of that term. It evokes images of cones and steel belts in most peoples minds, when in actuality, we don't have those in a Prius.