The artesonado ceiling in the throne-room of the Alhambra is known as the Seven Heavens, since it appears to represent the path traveled by the soul, passing through the seven heavens of the cosmos until reaching at the peak the eighth heaven of the Muslim paradise. This paper will discuss and analyze the geometric structure of the ceiling and its eight different types of star polygon designs. Using only the geometer’s tools of straightedge and compass (or the electronic equivalent, the Geometer’s Sketchpad software), skeletal versions of the star polygon designs will be reconstructed and classified according to the symmetry elements permitted.