Somanathapura temple , Karnataka : One of the most complete example of
Hoysala architecture with Vesara style Vimana
It is one I have to visit still along with sravanabelagola (jain monolith). We were supposed to visit both the same day we did (extended family road trip) visit to Belur and Halebid, I was 8 years old at time....but we ran out of time that day. Further visits later were other temples in other parts....there are just so many temples in this part of our country.
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To give more idea of the general Dravidian architecture theme (as it is prevalent for temples of all size, not just the very biggest ones)...
Closer to my hometown, is temple just a few minutes from where my mom was born:
It is just outside Coimbatore in a town called Perur.
In fact my mother's family are all connected to this temple largely. Her uncle was one of the priests, actually early memory of mine is when he took us on tour of temple and explained various local specialities and superstitions of the temple (each temple has some unique to it).... he also showed the elephant stable which had one of the resident elephants in it eating some sugar cane at the time. It was in a bit of mood so he didn't allow us to go too close to it.
The temple corridor is quite a well known one in Tamil Nadu for its size and detail relative to the complex:
The painted ceiling frescos telling religious+moral stories held by grand columns is noted internal feature of South Indian temples...along with strict agamic sanctum design.
Often I remember there will be elephant also standing (in sunlit area) as we enter this corridor, and you can get its blessing.
@Joe Shearer