An icosahedron-based method for pixelizing the celestial sphere

Abstract

For power spectrum estimation it's important that the pixelization of a CMB sky map be smooth and regular to high degree. With this criterion in mind the ``COBE sky cube" was defined. This paper has as central theme to further improve on this elegant scheme which uses a cube as projective base -- here an icosahedron is used in its place. Although the sky cube is excellent, a further reduction of 20 percent of the number of pixels can be obtained while the pixel distance is maintained, and without any degradation of accuracy for integration. The pixels are rounder in this scheme, where they are hexagonal rather than square, and the faces are small in this implementation which simplifies area-equalization. The reason distortion is lessened is that the faces are smaller and therefore more flat. To use the method, you can get a FORTRAN code from the Internet.