= Boxy and disky isophotes
{title2=$a_4\cos(4\theta)$}
Writing an <isophote>'s radial residual about its fitted ellipse as $\delta r=a_4\cos4\theta+\cdots$, 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.
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