Learned image codecs (LICs) achieve high reconstruction quality, but their decoding speed is often insufficient for immersive virtual reality (VR). Gaussian splatting (GS) codecs render much faster, yet still lag in reconstruction quality and typically decide primitive allocation without considering the coding cost of each primitive. We introduce OIC-GS, an omnidirectional GS codec with a new hierarchical HEALPix primitive grid representation. Gaussian primitives are anchored at predefined spherical locations, eliminating explicit coordinate coding. Finer levels refine their coarser ancestors, naturally supporting coarse-to-fine reconstruction and layered transmission. The predefined grid also enables efficient viewport decoding by selecting only view-relevant primitives. We further introduce a lightweight entropy model for quantized primitives and optimize the codec under a spherical rate-distortion objective. Primitives with insufficient rate-distortion benefit are automatically removed when their quantized opacity becomes zero, allowing OIC-GS to adapt both primitive density and level of detail without a fixed primitive budget. A single bitstream supports full-sphere, viewport-dependent, and progressive decoding. The first viewport reaches final quality after decoding only 52% of the bitstream, and is then rendered at 1,270 FPS. On a 100-image omnidirectional benchmark, OIC-GS outperforms all evaluated GS codecs, reducing WS-PSNR BD-rate by 49.6% over GaussianImage++ and 68.6% over SGI, which uses a learned entropy model.

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