An ellipsoidal dome is a dome (also see geodesic dome), which has a bottom cross-section which is a circle, but has a cupola whose curve is an ellipse.[1]
Ellipsoidal dome of Dhyanalinga
There are two types, the prolate ellipsoidal dome and the oblate ellipsoidal dome. A prolate ellipsoidal dome is derived by rotating an ellipse around the long axis of the ellipse; an oblate ellipsoidal dome is derived by rotating an ellipse around the short axis of the ellipse.[2]
Of small note, in reflecting telescopes the mirror is usually elliptical, so has the form of a "hollow" ellipsoidal dome.
The Jameh Mosque of Yazd has an ellipsoidal dome.[3]

Graphical illustration of an ellipsoidal dome. Note the blue and red "ellipses" are circles, at an angle. The blue and red ellipse is rotated, about its vertical axis. At top in blue is a prolate ellipsoidal dome.
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