Astypalaia is located between the Cyclades and Dodecanese groups of islands and sort of belongs to both.
It is commonly called "the butterfly" because of its shape, but I think that is a bit of a push. It does have two 'wings' that are joined by a very narrow strip of land, a hundred meters or so wide. Astypalaia means 'old city' but there is a myth (of course) explaining the name as one of the daughter of the gods.
Chora is the main, and by far the largest, settlement on the island. The photo above shows Chora to the right. To the left is Pera Yalos, the port (or one of them).
The island is connected by ferry and air but both are infrequent (maybe one a day) and the ferry can show up in the middle of the night.
There are a number of small beaches and settlements but this is a quiet island that is about 100 square km with a population in summer of about 1400. Much of the island is grazing or agricultural. It is easy to get away from everyone if you want to.
It might seem that this would be a boring place to go, but what happens is that I get involved in the small, the local and the specific and always find something interesting to do. Good island for hiking.
The official island website is here.