Boxy and disky isophotes ($a_4\cos (4\theta )$)

Writing an isophote's radial residual about its fitted ellipse as $\delta r=a_4\cos 4\theta +\cdots$, positive $a_4$ extends the major and minor axes and gives a pointed, disky shape; negative $a_4$ extends diagonal directions and gives a boxy shape. The sign stated here is for radial residuals, not an unconverted brightness residual. Massive slowly rotating elliptical galaxies commonly have boxy isophotes, while embedded rotating disks commonly make lower-mass elliptical galaxies disky.