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Quadrilateralized Spherical Cube (quad-cube) projections belong to the class of polyhedral projections in which the sphere is projected onto the surface of an enclosing polyhedron, typically one of the five Platonic polyhedra: the tetrahedron, hexahedron (cube), octahedron, dodecahedron, and icosahedron. The starting point for polyhedral projections is the gnomonic projection of the sphere onto the faces of an enclos-ing polyhedron. This may then be modified to make the projection equal area or impart other special properties. However, minimal distortion claims often made for polyhedral projections should be balanced against the many interruptions of the flattened polyhedron; the breaks should be counted as extreme distortions. Their importance in astronomy is not so much in vi-sual representation but in solving the problem of distributing N points as uniformly as possible over the sphere. This may be of particular importance in optimizing computationally intensive applications.
As defined by:Calabretta and Greisen, 2001
Research work was carried out at either the Astrophysics Research Insitute or Cardiff University Dept. of Physics and Astronomy.
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