A graphics system and method for processing geometry compressed, three-dimensional graphics data are disclosed. After transforming and lighting each vertex, a vertex data stream is decompressed using connectivity information, and vertexes are reassembled into geometric primitives. The connectivity information may include mesh buffer references, vertex tags, or other types of information. Independent buffers, queues, and / or caches are used to simultaneously store: (a) vertex data for the next several primitives, (b) vertex data that will be reused, (c) vertex tags, (d) control tags, (e) vertex data being assembled into a primitive, and (f) an assembled primitive ready to be launched. The assembled primitive may be clip tested for visibility in a defined viewport, before investing time to have the primitive processed into pixel data for display. The independent buffers, queues, and / or caches may also enable the vertex processing steps to be performed in parallel and at different rates.