Which fact is not true about the rhea?

Player #27643412, whilst the wording is a little unclear, a male builds one nest which all the females lay their eggs in, so no need to move around.

if they're polygamous, & the male has between 2 & 12 mates & he sits on the eggs, how is he going to move between all the nests to keep the eggs warm?.. There's a problem with this explanation, as wouldn't the eggs need to be kept warm all the time?