The Nice. Hellingon Rush is a team build designed to get an army of hellions and speedlings as fast as possible. Enabling shared controls allows another player to build an extractor, assimilator, or refinery the terran player can use to get hellions 30 seconds faster than doing it alone.
Two hellions complete at 4 minutes and 4 hellions at 4:30 in the fastest version. However, this involves cutting SCV production and the teamate building on the gas geyser has to be close enough to build it when the 8th SCV spawns. The terran builds a supply depot with his 8th SCV, starts mining vespene gas as soon as possible which should be just before the depot finishes and the terran begins building a barracks. The terran can squeeze out two more SCVs and have a little over 100 vespene gas to build the factory when the barracks finishes and start building a reactor on the barracks shortly after. It is best to upgrade to an orbital command while the factory is building. Swap the factory with the barracks and start buliding 2 hellions and use a mule to get more minerals. While building the 3rd and 4th hellions you should have enough minerals for a supply depot and be able to pump out hellions non-stop 2 at a time.
Economic versions of this build can easily be done by building on the vespene geyser slightly later. This still allows the terran to get hellions out faster than normal with a better economy which makes it easy to transition into seige tanks, banshees, or rush for infernal pre-igniter.