We demonstrate an active Sagnac ring interferometer that operates on the previously unexploited 3s2→2p6 (611.8 nm), 3s2→2p7 (604.6 nm), and 3s2→2p8 (593.9 nm) neon transitions, in a helium-neon gain medium. The cavity was constructed using state-of-the-art ion-beam sputtered, ultralow-loss supermirrors designed to yield greater transmission loss at lower optical frequency, which partially compensates for the gain differential across the three transitions. For an optimized cavity fill of 0.3 mbar partial pressure of neon (50% Ne20 and 50% Ne22) and a total gas pressure of 2 mbar, for laser operation at 611.8 nm, the cavity Q is 1.2×1011, having a cold cavity ringdown time of 38 μs. The laser yielded a stable Sagnac frequency of 117.4 Hz due to the Earth's rotation. The usable gyroscopic sensitivity is determined to be 8.8×10-9 rad/s for a measurement time of 128 s.