Topi have been seen sleeping with their mouths on the ground and their horns pointing straight up. It may be a way to stay safe.

Antelopes of Africa · day 6 of 7
They rest their mouths on the ground with horns aimed at the sky.
It coats grass stems in the oil and waves them so it falls on its head.
They stand in parallel ranks, eyes closed, bobbing their heads.
The dominant female may take over his role and chase off outsiders.
Fresh green plants usually give it enough water.
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