Howdah

A howdah was a kind of a saddle used on elephants in India. It strapped on to the beast and was canopied, but with open sides. Box-shaped, their design allowed for two people to ride next to each other. They were often elaborately decorated, as with tassels.

The Tenth Doctor and Donna Noble used a howdah when they travelled by elephant with Gandhi. (NSA: Ghosts of India)