It is unprecedented for all 11 Justices to sit for a single case and that is saying a lot for an institution that in one guise or another has existed for more than 600 years.
But, judging so far from the furore greeting the judiciary's involvement in Brexit, it may be a case of safety in numbers.
Howls of protest and anger from Brexit-supporting politicians and newspapers greeted the decision by the High Court on 3 November that Parliament must vote on Article 50 before it can be triggered.
But the Supreme Court has made it clear that it is highly unlikely to be swayed by such considerations when it starts its deliberations on 5 December.
In an exclusive interview with the BBC, one of the judges, Lord Kerr of Tonaghmore, confessed to feeling unabashed by the predicted public and press interest in the case.
"I think that it's not a question of my looking forward to it but I can perfectly well understand why the public is extremely interested in it," he told me.
"And that's a good thing. Our communications staff and our reception staff are well prepared to cater for that public interest and to ensure that as much facility for those who are interested in it is provided, so that the public can hear the arguments as they are presented.
"I think that's an entirely healthy thing. So I'm not particularly looking forward to the public interest but I'm certainly not disheartened by it."
The government appealed to the Supreme Court after a "lower court", in this case the High Court,  ruled that Parliament must vote before the triggering of Article 50.
The High Court had upheld the challenge by businesswoman Gina Miller that Prime Minister Theresa May had no authority by use of the Royal Prerogative to start the process of the UK leaving the EU.
Several Brexit-supporting newspapers attacked the decision, with the Daily Mail describing the judges as "enemies of the people".
Lord Kerr declined to comment about the newspaper headlines but said: "I think the important message that I would like to convey is that we as judges apply the law.
"We are not involved in reaching decisions based on anything other than the legal principles as they are presented to us and the legal analysis which we conduct as to these extremely difficult and complicated questions.
"That's not to say that we don't have personal views but we are all extremely conscious of the need to set aside our personal views and to apply the law as we conceive it to be."
The Supreme Court is based in Parliament Square next to both Westminster Abbey and the Houses of Parliament.
The court formally began in October 2009 housed in a building previously used as a crown court. Before 1965 it was home to Middlesex County Council, which was officially abolished in a reorganisation of London's local government.
The Supreme Court took over the functions of the Appellate Committee of the House of Lords and its justices also sit as the Judicial Committee of the Privy Council and as such will occasionally hear appeals against the death penalty from Commonwealth countries.
More than 100,000 people visit the court each year and more than 350 schools take part in tours and sit in on its many hearings.
The building was refurbished to allow a lot of light and colour and houses a cafÃ©, an exhibition area and even a rather funky carpet designed by Sir Peter Blake, who famously designed the cover for the Beatles' Sergeant Pepper Album.
Former Poet Laureate Sir Andrew Motion was commissioned to write a poem, which has been chiselled into stone benches outside the court building.
In an average year, the Supreme Court hears around 90 appeals and makes around 80 judgements on important issues of law that shape the way everybody lives, while it also upholds and dismisses appeals in almost equal proportions.
On either side of the Atlantic, there is much talk of elites.
The Supreme Court is open but not at the moment as diverse or representative as it wishes to be.
There is only one woman justice and Oxbridge and public schools feature prominently in the background of most of the justices.
Lord Kerr concedes it is a problem, saying, "Well we're not diverse enough in the sense that we don't reflect the gender balance of the community for a start.
"Nor do we reflect the ethnic population of the United Kingdom and that's something that we are concerned about and that we're working towards.
"Curiously enough, I think possibly I represent a particular part of diversity in that I come from Northern Ireland first of all.
"Secondly I wasn't educated in a public school, I didn't go to Oxbridge, and I certainly don't lead a privileged life.
"I was one of a family of seven, of a widowed mother. Happily I was able to go to university but I don't think that I could be described - certainly in terms of background - as coming from an elite."
All 11 senior judges of the Supreme Court of the United Kingdom will decide the most significant British constitutional question for years - whether the government has the power to trigger Article 50 of the EU Lisbon Treaty to begin Brexit.