The sequence of facets and nodes has a direct influence on the efficiency ofaccess to spherical triangle region quadtree. Based on the labeling schema by Lee, spatial curves both for facets and nodes are proposed and the main algorithms for coordinate translation, node L sequence generation and visiting nodes are presented. In particular, constant time algorithms for generating node L sequence are advanced by using bit manipulation operations, which can be easily implemented with hardware. In L curve the distance between three nodes of a facet is mostly limited in a range of small value, thus making fast access possible. Though codes of sibling facets are continuous, the difference between codes of some cousins may occasionally be very large and makes the distance of a few facets also very large, thus greatly increasing the mean node distance and the total traversing distance. Therefore an m cluster of nodes is proposed as a basic storage unit for n cluster, which should store every shared node in each, and the distance between three nodes of a facet is limited to a controllable scope.