Quadrilateralized spherical cube

In mapmaking, a quadrilateralized spherical cube, or quad sphere for short, is an equal-area polyhedral map projection and discrete global grid scheme for data collected on a spherical surface (either that of the Earth or the celestial sphere).

It was first proposed in 1975 by Chan and O'Neill for the Naval Environmental Prediction Research Facility.

The vertices of the cube correspond to the cartesian coordinates defined by |x|=|y|=|z| on a sphere centred at the origin.

The quad sphere projection does not produce singularities at the poles or elsewhere, as do some other equal-area mapping schemes.

Distortion is moderate over the entire sphere, so that at no point are shapes altered beyond recognition.