Howdah

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

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