If you're talking about the structure:
* Conical dwelling: This is a more formal, descriptive term.
* Tent: This is a general term, but it could work if the context is clear.
* Tipi: This is the more accurate spelling of the word, though it might be less familiar to some readers.
* Lodge: This can be used for a variety of dwellings, but it could work if the teepee is being used as a permanent or semi-permanent residence.
If you're talking about the cultural significance:
* Traditional dwelling: This emphasizes the historical and cultural importance of the teepee.
* Native American home: This is a more general term that acknowledges the cultural origin of the teepee.
The best synonym to use will depend on the specific context and the level of formality you want to achieve.