They don't call such entanglements threesomes at international summits, of course, where the participants are so polite, at least in public, they have to practise gymnastics with the very language of the thing.

Consider the term "communique". It's a rather pretty French word – French being the language of both love and diplomacy – used to describe a sheaf of papers whose words speak of consensus but obscure the hard separate ambitions and weaknesses of powerful nations and the backroom wrangling and squabbling from which it is woven.

A threesome at the G20 is known as a trilateral, which has the advantage, at least, of sounding muscular. Tony Abbott found himself in the middle of a particularly muscular trilateral on Sunday, with the President of the most powerful nation on Earth at his right hand and the Prime Minister of the third largest
national economy at his left.

None of them quite knew what went where, least of all Mr Abbott, as they went through the preliminaries for the cameras. It devolved into an awkward cross-body handshake between Mr Abbott and Japanese Prime Minister Shinto Abe, and a much more awkward wrist grasp with US President Barack Obama.

Rather than draping his spare left arm around Mr Abbott, President Obama grasped his own left elbow, everyone smiling frantically in the hope it would be over, and soon, as if it were a blind date gone dreadfully wrong.

By the end of this weekend, about the only consensus between Mr Abbott and President Obama on the subject of climate that Mr Abbott, the host, hadn't wanted discussed, was that Brisbane's heatwave was a sizzler.

Offstage, Russian President Vladmir Putin, for whom the G20 had been a mono-lateral, boarded his plane and roared into the sky hours before the communique was even communicated. Whatever Brisbane's soaring temperature, he'd been frozen out. Winter in Moscow would be warmer.

And yet, at the end, despite all the contortions required and the polite wording, the Group of the world's 20 biggest economies, most of which had managed to spin into disaster during the Global Financial Crisis and beyond, had agreed to embrace policies designed to increase GDP by at least 2 per cent by 2018.

"Raising global growth to deliver better living standards and quality jobs for people across the world is our highest priority," the G20 began its breathlessly awaited communique.

The members had signed off on no less than 800 separate reforms and measures to make this occur – a document known as the Brisbane Action Plan – and they promised "peer review" in the hope that all this reform might occur.

The trick now is to work out what goes where in this great plan. When something as simple as a staged trilateral handshake can end up looking like an octopus suffering rictus, a resolution by 20 participants to "lift economic growth, support job creation, promote development and build global confidence" seems courageous, at the very least.