HiPS tiles and pixels. A HiPS structure is defined by a set of tile orders k_tile and by the number of pixels along each side of the tiles n_tile. Here we show an orthographic projection of the sphere shaded to indicate different orders, and highlighting in black three individual HiPS tiles of orders k_tile = 3, 4 and 5, with pixel tiling of n_tile = 512. Note that HiPS representations of astronomical data usually start with k_tile = 3 as the lowest order tile, and each successive order of smaller tiles is a higher resolution representation of the data. Some characteristics of the tiles are shown in the expanded view of the tiles on the right of the figure, including the approximate side length of the tile θ_tile (defined as the square root of its area ). The number of pixels inside a tile is constant over all of the orders, and in this example where n_tile = 512 each tile comprises 512 × 512 pixels. The pixels inside a tile correspond to a higher order HEALPix grid, and in this example k_pix = k_tile + log ₂n_tile = k_tile + 9, so that the k_tile = 3 tiles are filled with 51.̋55 pixels that correspond to a HEALPix grid of order 12.