Yellow Gem (Hotel)
Enter the main hotel, look up, and climb the shelves into the vent duct network. Follow the duct to the dead-end pipe to find the Yellow Gem.
Blue Gem (Canyon)
Walk to the midpoint of the canyon bridge, drop straight down, and land on the southern ice cliff shelf to pick up the Blue Gem.
Purple Gem (Research Tower)
Climb to the third floor of the Research Tower, walk behind the secondary mainframe computers, and look between the support columns and the exterior glass.
Green Gem (Factory)
Find the water-routing pipelines beneath the central catwalks, drop onto the copper manifold pipe, and walk the pipe to the gem.
Red Gem (Lava Pit)
Walk the stone retaining slabs around the primary lava furnace and look on the ash block behind the exhaust valve.