Sparse Convolution (SpC) powers 3D point cloud networks widely used in autonomous driving and augmented/virtual reality. SpC builds a kernel map that stores mappings between input voxel coordinates, output coordinates, and weight offsets, then uses this map to compute feature vectors for output coordinates. Our work identifies three key properties of voxel coordinates: they are integer-valued, bounded within a limited spatial range, and geometrically continuous, i.e., neighboring voxels on the same object surface are highly likely to exist at small spatial offsets from each other. Prior SpC engines do not fully exploit these properties and suffer from high pre-processing and post-processing overheads during kernel map construction. To address this, we design Spira, the first voxel-property-aware SpC engine for GPUs. Spira proposes (i) a high-performance one-shot search algorithm that builds the kernel map with no pre-processing and high data locality, (ii) an effective packed-native processing scheme that accesses packed voxel coordinates at low cost, (iii) a flexible dual-dataflow execution mechanism that efficiently computes output feature vectors by adapting to layer characteristics, and (iv) a network-wide parallelization strategy that builds kernel maps for all SpC layers concurrently at network start. Our evaluation shows that Spira significantly outperforms prior state-of-the-art SpC engines by 1.68x on average and up to 3.04x for end-to-end inference, and by 2.11x on average and up to 3.44x for layer-wise execution across diverse layer configurations. The source code of Spira is freely available at github.com/SPIN-Research-Group/Spira.