Recumbent trikes with full fairings came from human powered vehicle (HPV) racing. One was Mike Burrow’s Windcheetah, originally intended as a stable HPV trainer for HPV racers. Recumbent enthusiasts soon discover the advantanges of a fully faired trike for commuting compared to a full faired recumbent bike. There is no need to balance the vehicle at stops, no worries of side wind blowing the vehicle around.
Velomobile became the term used to describe these fully faired recumbent trikes built for commuting in traffic and offering all-weather protection.
One of the most well know is the Leitra, with a flip-forward front section that allows entry and exit of the rider.
Check out velomobile.net for more info on velomobiles.