Tessellation of a sphere according the HEALPix scheme. In this figure the pixel resolution corresponds to N_side = 4 (N_pix = 192). Almost every pixel in a HEALPix map has 8 neighbors; however, a few pixels only have 7 of them. In this figure, the blue pixel has 7 neighbors, while the green one has 8. Black dots represent pixel centers; seven-neighbor pixels are highlighted with grey diamonds. These pixels are at the intersection of three base-pixels (delimited using thick lines); this kind of intersection occurs only near the two polar caps, and in any map with N_side ≥ 2 there are exactly 8 of them. Thus, the number of seven-neighbor pixels is always 24 (because of the nature of the orthographic projection used in this sketch, only 9 seven-neighbor pixels are visible).