Triremes are described by Plato as being part of the Atlantean navy. However, the existence of triremes is completely incompatible with a 9600 BC date for the destruction of Atlantis as triremes were only developed around 9,000 years later. Triremes were built of lightwoods and were designed for a day’s travel at a time (50-60 miles) as onboard facilities were quite limited and could be easily beached at night.
Triremes were top-heavy and somewhat prone to toppling over in a violent storm. Consequently, they were considered to be fair-weather vessels and were not generally used in winter(c).
It is likely that Plato used the term trireme to make the story more relevant to his Athenian audience.
In 1987 a fullscale copy of a trireme, Olympias, was launched(a). The ship is due to visit New York in 2012(b). A book describing the construction and trialing of the Olympiasis also available(d).

Olympias
(a) http://purplemotes.net/2007/02/11/science-in-action-the-trireme-olympias/
(b) http://www.futurecareinc.com/news/trireme-in-new-york-city/
(c) http://www.indepthinfo.com/salamis/triremes.shtml

