Howdah

A howdah was the carrier on the back of elephants in India. (TV: "The Watcher") 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. (PROSE: Ghosts of India)

The First Doctor mentioned to Steven Taylor that if the TARDIS's chameleon circuit was functioning correctly, the TARDIS would possibly take the form of a howdah if they landed during the Indian Mutiny. (TV: "The Watcher")

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