when were these caves constructed?
Between the 5th and 9th century.
Elephanta Caves
These date them between 5th and 9th century, and attribute them to various Hindu dynasties. 
cave temple of elephanta are dedicated to which god It is dedicated to the Hindu god Shiva. where is this cave located? They are on Elephanta Island, at Mumbai Harbour. how many islands are connected to this harbour? Six. and when was it opened? UNANSWERABLE does this harbour contribute to any pollution? Yes, heavy metals flux are found in the creeks adjacent to the harbour, and the harbour acts as a sink for most of the pollutants.
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Elephanta Caves [SEP] Introduction
The caves are hewn from solid basalt rock. Except for a few exceptions, much of the artwork is defaced and damaged. The main temple's orientation as well as the relative location of other temples are placed in a mandala pattern. The carvings narrate Hindu mythologies, with the large monolithic Trimurti Sadashiva (three-faced Shiva), Nataraja (Lord of dance) and Yogishvara (Lord of Yoga) being the most celebrated. These date them between 5th and 9th century, and attribute them to various Hindu dynasties. They are more commonly placed between 5th and 7th centuries. Most scholars consider it to have been completed by about 550 CE.