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I've heard "handegg" before but a football is not shaped like an egg, it's vaguely egg-like but the teardrop shape of an egg is distinctly not what a football looks like.

It looks more like an egg than it looks like a ball, so if we have to force fit into a common word, my vote goes for egg

But it acts more like a ball than like an egg.

Or just American Handball

Or just go back to calling it gridiron football.