can i sleep at sydney airport?

No the airport (this side of customs) closes for 4 hours every day. If you are waiting in transit for an international connection you can stay THAT SIDE of customs but our side - everyone has to get out (so no hiding in the prayer room).

The airport opens again at 5am so you only have to find somewhere for 4 hours.

You cant sleep there, no. But there are hotels at the airport that you can stay at. If you are looking for a cheap option, Formule 1 has a hotel at the airport, they are generally about 60-70 dollars a night. But it saves on the taxi/bus/train fare, and they are always more expensive when going to the airport itself

there are a number of resorts close to the airport alongside with a Hilton and a Travelodge. All furnish shuttles to and from the airport, wake-up calls, early breakfasts etc. After a 20 hour flight, I anticipate you particularly won't prefer to spend time observing Sydney's nightlife. in case you do prefer to flow out then e book a motel interior the city - in addition they furnish shuttles to the airport.

There's nowhere at the airport where you can "officially" sleep, why do you think they have all those expensive hotels all around the area? :)

If you are really stuck, there is a prayer room on level 3 of Terminal 1 (International). If anyone kicked you out of there, it would be harsh. The link below may help.

i'm fairly sure that sydney airport isn't open 24hrs which means it closes; requiring everyone in it to leave- meaning you probably cant sleep there. your best beat would be finding a youth hostel; most have 24hr check in and are cheap as well as safe for people of all ages. just google youth hostel and sydney australia for heaps of options.